Google
This is a digital copy of a book that was preserved for generations on library shelves before it was carefully scanned by Google as part of a project
to make the world's books discoverable online.
It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject
to copyright or whose legal copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books
are our gateways to the past, representing a wealth of history, culture and knowledge that's often difficult to discover.
Marks, notations and other maiginalia present in the original volume will appear in this file - a reminder of this book's long journey from the
publisher to a library and finally to you.
Usage guidelines
Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the
public and we are merely their custodians. Nevertheless, this work is expensive, so in order to keep providing tliis resource, we liave taken steps to
prevent abuse by commercial parties, including placing technical restrictions on automated querying.
We also ask that you:
+ Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for
personal, non-commercial purposes.
+ Refrain fivm automated querying Do not send automated queries of any sort to Google's system: If you are conducting research on machine
translation, optical character recognition or other areas where access to a large amount of text is helpful, please contact us. We encourage the
use of public domain materials for these purposes and may be able to help.
+ Maintain attributionTht GoogXt "watermark" you see on each file is essential for in forming people about this project and helping them find
additional materials through Google Book Search. Please do not remove it.
+ Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Do not assume that just
because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other
countries. Whether a book is still in copyright varies from country to country, and we can't offer guidance on whether any specific use of
any specific book is allowed. Please do not assume that a book's appearance in Google Book Search means it can be used in any manner
anywhere in the world. Copyright infringement liabili^ can be quite severe.
About Google Book Search
Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers
discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web
at |http: //books .google .com/I
>
%
S
^
Stables and rules
FOR FACILITATING THE CALCULATION
EARTHWORK,
LAND, CURVES,
DISTANCES, AND GRADIENTS,
REQUIRED IN THE FORMATION
OF
RAILWAYS,
ROADS, AND CANALS:
ALSO,
ESSAYS
ON THE PRISMOIDAL FORMULA,
AND
ON THE POWER REQUIRED UPON INCLINED PLANES.
BY J. B. HUNTINGTON,
A880CIATB OP THB INSTITUTION OF CIVU< BVaiNBBRS.
>■
*i:
LONDON:
*:? PUBLISHED FOR THE AUTHOR.
BY JOHN WEALE, HIGH HOLBORN.
[entered at stationers' hall«]
1846.
Vriot Twenty-four Shillingt.
•v
M
*..t
TfUtportatlon
Library
TA
LONDON:
PRINTED BY JOSEPH ROGERSOM^
94, VOBVOLK 8T&BBT, 8TBAKD.
t
Libra ly
PREFACE.
•
The great advancement made of late years in the sci-
ence of civil engineering, and the increased number of
works promoted by public and private interests, in the
formation of roads, canals, and railways, call for a
more extended view of the theory of the construction
and measurement of such works than has hitherto been
given to the world, both for the better instruction of
pupils, and for the facihtation of the labours of practical
men. With the above object in view I have prepared
the following work, especially adapted to the " measure-
ment" of railways, and comprising in its extent a
greater compilation of Tables and Essays, on the impor-
tant features of this subject, than has hitherto been
introduced.
During the process of calculating the cubic quantity
of earthwork requisite to form a given embankment,
or to be taken from a given cutting, I have found the
usual methods proposed in various authors and geome-
tric writers more or less tedious in their application ;
and in the more improved works furnished to the public.
II
the extent of the tables has not been sufficient, in some
instances, to enable them to be serviceable.
Calculations of this description are frequently required
on a very short notice ; and then, on account of the
multiplicity of figures employed, an easy and accurate
method is an object, not only because time is saved,
but amongst so many evolutions of numeration, a ready
method would greatly tend to prevent errors to which
a lengthened process is liable ; and I hope that, on a
fair investigation into the merits of my manner of treat-
ing this subject, practical men, both engineers and
contractors for works, may judge favourably of the
utility of my labours.
The portion of the work devoted to the calculation
of earthwork contains " Tables for all Bases, between
Base 20 and Base 36 inclusive, adapted to ten different
Slopes." The tables are followed by an " Essay on
the Prismoidal Formula," and a full " Explanation of
the use of the Tables," with a digest of all the " Rules
derived from the Essay." "Tables for calculating
Areas of Land" and " Areas of Slopes" are next given,
accompanied by an " Explanation." Then follows a
set of " Tables for calculating Offsets to Curves," and
an "Explanation" of its use, together with a short
"Table to find the Radii of Curves," and "Rules
relating to Curves." Next to this comes a "Table
of Distances," and then a "Table of Gradients,"
with the necessary " Explanation and forms of use."
Ill
I conclude the work with an " Essay on the Power
required on IncKnes/* in which all the circumstances of
Friction, Atmospheric resistance. Gravity, Loss of power
round Curves and by the action of the Wind, are all
separately considered.
In order to give a general notion of the various
conditions which the Earthwork of a Railway exhibit,
I have prefixed a Frontispiece, which, in a bird's-eye
view, pourtrays a cutting ^ with the eflFect produced by
^ding ground, and a hench formed on the highest side,
at a certain height, extending along the cutting, parallel
with the base, till it meets the surface of the ground ;
also an imfinished embankment, with the foreground
iflustrating the fencing off of the requisite land, and
other minor points of appearance.
The great object I have endeavoured to keep in view
has been utility , especially to students in Civil Engi-
neering. I have, therefore, avoided all subjects the
investigation of which is merely iogenious without
practical aim. Entire novelty of matter is hardly to be
expected in a work of this nature ; but I humbly hope
that, in general, the reader will not feel disappointed in
this respect.
In choosing the t3rpe of this work, especially for the
tables, my object was to obtain a bold, clear figure,
which should admit of being easily read off; in which
important desideratum, I trust, the reader will admit
that I have succeeded.
All the calculations will be founded on theories
derived from or confirmed by practical observations ;
and the data, where assumed in illustration of the rules,
will be such as may be considered an average, but
which, owing to the many complex and inappreciable
difficulties which invest discussions such as are con-
tained in this volume, may be varied by the judgment
of the reader. The work is so arranged, that the por-
tion relating to the Calculation of Earthwork can be
separated, and two volumes can be made up instead of
one, to suit the convenience of the reader. I request
indulgence for such irregularities and errata as may
occur in the composition of the essays; and I will gladly
acknowledge any communications and corrections, and
insert them in subsequent volumes.
J. B. HUNTINGTON.
Wamtead, Eaaex,
March \8t, 1846.
CONTENTS.
EARTHWORK.
Page.
(S
Tables for calculating Earthwork, from Base 20 to Base
36, with Slopes i to 1, ^ to 1^ | to 1, 1 to 1, li to 1, li to 1,
lito2to l,2^to l,3to 1 1
Tables for Base 20 1
11
21
31
41
51
61
71
81
91
101
..' Ill
121
131
141
151
161
m
173
173
l74
21
22
23
24
25
26
27
28
29
30
31 '
32
33
34
35
36
Table of Bases only
Prismoidal Formula (Essay on the)
Prismoid (Description of)
Section (Description of) •
Rule for computing Prismoid, as given in Books of Geometry... . 176
Proof of the above rule by the method of Fluxions 176
Proof of the Rule by Geometric demonstration . .• 178
Prismoidal Formula compared with the method of computing by
McanHeights 179
€t
(t
S(
(S
ft
tt
{f
<(
((
€t
f«
<«
<C
((
ft
VI CONTENTS.
Page,
Prismoidal Formula compared with the method of computing by
Mean Areas 180
Examples in illustration of the above Rules 181
Cross Sections illustrated 184
Areas of Prismoid, with imiform Sloping Cross Sections (Rule for
finding) 187
Ditto, Rule compared with the Rule for Level Ground 188
Cubic Contents of Prismoids, with uniform Sloping Cross Sections
(Rule for finding) '; *188
Ditto^Rule compared with the Rule for Level Ground 189
Areas and Cubic Contents of Prismoids, with ^'ariable Cross
Sections (Rules for finding) 190
Areas of Prismoids, with curving Cross Sections (Rule for finding) 192
Rule for Prismoids with two dififerent Slopes 193
Rule for finding the Cube due to an alteration of Level of the
Base Line 194
Rule for the Area of the Prismoid when Benches are introduced. . 195
Rule for Area of the Prismoid when the Widths at the Surface are
given instead of the Heights • 196
Rule for the Cubic Contents of the Prismoid, as above 197
Rule for the Area of the Prismoid, with uniform Sloping Cross
Sections . « . » 198
Rule for the Cubic Contents of the Prismoid, as above 199
Practical Rules derived from the Essay relating to the
Prismoidal Formula (Compilation of) 199
Explanation of the use of the Tables 203
Examples by MacNeil's Tables of Earthwork 204
][lule for forming MacNeil's Tables of Earthwork 204
Rule for forming the Tables of Earthwork in this Work 205
Rule to calculate the Cube of a Prismoid by the Tables 205
Form of arranging a series of Calculations for a Railway, &c.. . . . 207
Rule to calculate the Area of a Prismoid by the Tables 208
Role to calculate the Area of the Sides of a Prismoid by the
Tables. 208
Rule to calculate the Cubic Contents of a Prismoid when the Base
is altered 209
Rule to calculate the Area of a Prismoid when the Base is altered 209
CONTENTS. Vll
Page.
Explanation of a Scale for calculating Earthwork 210
Application of the above Scale 211
Rule for constructing the above Scale. . 211
LAND.
Tables for calculating the Areas of Land 213
Tables for calculating the Areas of Slopes 218
Explanation of the Tables for calculating Areas of Land 223
Explanation of the Tables for calculating the Areas of Slopes .... 224
CURVES.
Tables of Offsets to Curves, for a Radius = 1000 225
Explanation of the Tables of Offsets to Curves 228
Rule for calculating Offisets 229
Rule for the use of the Tables of Offsets 229
Examples of the preceding Rule 230
General Rules for calculating Tangents, Offsets, Chords, and
Radii of Curves 231
Rule for calculating the Radius when the Tangent and
Angle are given 232
DISTANCES.
•
Explanation of the Table of Distances 233
Tables op Distances in Miles, Chains, Yards, and Feet 234
Tables of Distances in Feet, Chains, and Yards 337
Tables of Distances in Yards, Chains, and Feet. . « 237
GRADIENTS.
Tables of Gradients 239
Explanation of the Table of Gradients , 246
Form for arranging lists of Gradients 247
Rule to find the Gravitation of 1 Ton on a given Incline 247
Form for arranging the Power required to overcome Gravitation. . 249
Rule for computing the average Gravitation of 1 Ton over a series
of Inclines 250
POWER.
Essay on the Power required to move a given Load
ALONG Inclined Planes , 251
▼lU CONTBNTS.
Page.
Reristance due to Friction 251
Resistance of the Air 252
Table for computing the Resistance of the Air 260
Resistance due to the Gradient 261
General Rule for the total Resistance 262
Power of the Engines required to draw a given Load 263
Adhesion of the Engine Wheels to the Rails 264
Vaporization of Water of the Engines 265
Power of the Engines 266
Power on an Incline compared with that on a Level 267
The duty one Engine can perform 267
Table of Vaporization of Water^ and the Power of the Enjj^e under
various Pressures 268
Capability of an Engine (Causes of variation of) , 268
Accidental Causes of Resistance 270
Resistance of the Wind 270
Rules for calculating the Resistance of the Wind 274
Resistance of Curves 275
Centrifugal Force round Curves 276
Elevation of Outer Rail round Curves . . 277
Impingence of the Wheels against the Rails 278
Conical Form of the Tires of the Wheels 279
Rule for finding the Force of Impingence against the Rails 281
Rule to find the number of Oscillations per second due to the
Impingence 281
Rule to find the Resistance of a Curve (generally) 283
Table for estimating the Variations of the above Rules/ consequent
upon an increased distance between the front and hind wheels 285
Rule to find the Resistance of a Straight line 285
Conclusion 28 5
Errata :
P^^ 237— /or << yards into chains and feet/' read ''feet into chains
and yards."
Page 238— /or ''feet into chains and yards/' read "yards into
chains and feet/'
ERRATA.
In page v., after \\ to, insert 1.
187> /tne ;j, after W and B^, instead qf + read x .
193, Une 24, instead ofr + 9, read r ± s.
198, Une 13, instead of r •»■ '1, reoc^ i^ + 1*
200, ftite 20, instead of L, reocf Z.
202, tt»e 3, instead of r^ + 1, reod rs \/r«~^ 1.
202, rule 12, in the margin, instead of s, reoc^ 3.
208, Une 13, ti»feaii of chasm or, read chance of.
210, Une 11, instead of WBS, read were.
231, role 3, in the margin, instead of AD'' AB^
rearf AD« — AB».
236, Une 21, instead of 2|, read 2f .
260, Itne 27, instead qf role, reacf rise.
ft
99
99
99
(
BASE 20— SLOPE 1 to 1.
Add.
1
Add.
if. of
Dedact.
"a
Deduct.
K
33
1
31
1
0.3750
31
16.9306
.0015
1.4830
2
0.7592
82
16.5925
2
.0062
32
1.6802
3
1.1527
33
17.2638
3
.0139
33
1.6805
4
1.5555
34
17.9444
4
.0246
34
1.7839
5
1.9675
35
18.6342
5
.0385
36
1.8904
6
2.3888
36
19.3333
6
.0555
36
2.0000
7
2.8194
37
20.0416
7
.0766
37
2.1126
8
3.2592
38
20.7695
8
.0988
38
2.2284
9
3.7083
39
21.4861
9
.1250
39
2.3472
10
4.1666
40
22.2222
10
.1643
40
2.4691
11
4.6342
41
22.9675
11
.1867
41
2.6941
12
6.1111
42
23.7222
12
.2222
42
2.7222
13
6.6972
43
24.4861
13
.2608
43
2.8545
14
6.0925
44
25.2592
14
.3025
44
2.9876
16
6.5976
45
26.0416
15
.3472
46
3.1260
16
7.1111
46
26.8333
16
.3961
46
3.2654
17
7.6342
47
27.6341
17
.4460
47
3.4089
18
8.1666
48
•28.4444
18
.5000
48
3.6555
19
8.7083
49
29.2638
19
.5571
49
3.7052
20
9.2592
60
30.0925
20
.6173
50
3.8680
21
9.8194
61
30.9305
21
.6805
51
4.0139
22
103888
52
31.7777
22
.7469
52
4.1728
23
10.9675
63
32.6342
23
.8163
53
4.3349
24
11.6555
54
33.5000
24
.8889
64
4.5000
25
12.1627
55
34.3760
25
.9647
65
4.6682
26
12.7592
56
35.2692
26
1.0432
66
4.8396
27
13.3750
57
36.1627
27
1.1250
67
5.0139
28
14.0000
68
37.0555
28
1.2099
68
5.1913
29
14.6342
59
37.9675
29
1.2978
69
6.3719
30
15.2777
60
38.8888
30
1.3889
60
B
5.6556
(ii.)
BASE 20— SLOPE i to 1.
•53
Add.
1
Add.
"a
Dednct.
Dednct.
cn
1
s
Q*^
a"
.3796
31
20.3796
1
.0031
31
2.9660
2
.7777
32
21.3333
2
.0123
32
3.1605
8
1.1944
33
22.3055
3
.0278
33
36111
4
1.6296
34
23.2962
4
.0494
34
3.6679
5
2.0833
35
24.3055
6
.0772
36
3.7808
6
2.5555
36
263333
6
.1111
36
4.0000
7
3.0462
37
26.3796
7
.1512
37
4.2253
8
3.5555
38
27.4444
8
.1975
38
4.4568
9
4.0833
39
28.62T7
9
.2500
39
4.6944
10
4.6296
40
29.6296
10
.3083
40
4.9383
11
5.1944
41
30.7600
11
.3734
41
5.1883
12
6.7777
42
31.8888
12
.4444
42
5.4444
13
6.3796
43
33.0462
13
.6216
43
6.7067
14
7.0000
44
34.2222
14
.6049
44
5.9753
16
7.6388
46
36.4166
15
.6944
45
6.2500
16
8.2962
46
36.6296
16
.7901
46
6.6308
17
8.9722
47
37.8610
17
.8920
47
6.8179
18
9.6666
48
39.1111
18
1.0000
48
7.1111
19
10.3796
49
40.3796
19
1.1142
49
7.4104
20
11.1111
50
41.6666
20
1.2346
50
7.7160
21
11.8610
61
42.9722
21
1.3611
61
8.0277
22
12.6296
62
44.2962
22
1.4938
62
8.3456
23
13.4166
63
45.6388
23
1.6327
63
8.6697
24
14.2222
64
47.0000
24
1.7778
64
9.0000
25
16.0462
66
48.3796
26
1.9296
55
9.3364
26
16.8888
66
49.7777
26
2.0864
66
9.6790
27
16.7600
57
61.1944
27
2.2600
67
10.0277
28
17.6296
68
62.6296
28
2.4197
58
10.3827
29
18.6277
59
64.0833
29
2.6956
59
10.7438
30
19.4444 60
55.5656
30 2.7778
60
11.1111
( 111.
)
BASE 20— SLOPE | to 1.
4d
•a
•s
Add.
1
Add.
o •
Deduct.
Dednct.
X
31
1
Q*
1
.3842
24.8287
.0046
31
4.4490
2
.7962
32
26.0740
2
.0185
32
4.7407
3
1.2361
33
27.3472
3
.0416
33
6.0416
4
1.7037
34
28.6481
4
.0740
34
6.3618
5
2.1990
35
29.9768
6
.1157
36
66712
6
2.7222
36
31.3333
6
.1667
36
6.0000
7
3.2731
37
32.7175
7
.2268
37
63379
8
3.8518
38
34.1296
8
.2963
38
6.6851
9
4.4583
39
35.5694
9
.3750
39
7.0416
10
6.0925
40
37.0370
10
.4630
40
7.4074
11
6.7546
41
38.5324
11
.5602
41
7.7824
12
6.4444
42
40.0555
12
.6667
42
8.1666
13
7.1620
43
41.6064
13
.7824
43
8.6612
14
7.9074
44
43.1851
14
.9074
44
8 96-29
15
8.6805
45
44.7916
15
1.0417
46
9.3750
16
9.4814
46
46.4259
16
1.1852
46
9.7962
17
10.3101
47
48.0879
17 1.3379
47
10.2268
18
11.1666
48
49.7777
18
1.5000
48
10.6666
19
12.0509
49
51.4952
19
1.6713
49
11.1157
20
12.9629
50
53.2407
20
1.8518
60
11.5740
21
13.9033
51
55.0138
21
2.0417
51
12.0416
22
14.8703
62
56.8148
22
2.2407
52
12.5186
23
15.8657
63
58.6435
23
2.4491
53
13.0046
24
16.8888
64
60.5000
24
2.6667
54
13.6000
25
17.9398
65
62.3842
25
2-8935
56
14.0046
26
19.0186
56
64.2962
26
3.1296
56
14.5185
27
20.1250
57
66.2361
27
3.3750
57
15.0416
28
21.2592
58
68.2037
28
3.6296
58
15.5740
29
22.4212
59
70.1990
29
3.8935
69
16.1167
30
23.6111
60
72.2222
30
4.1667
60
16.6666
(iv.
)
BASE 20 SLOPE 1 to 1.
1.
Add.
■4^
-a
•53
Add.
Deduct.
<4H
Deduct.
1
W
Q*
Q
.3888
31
29.2777
1
.0062
31
5.9321
2
.8148
32
30.8148
2
.0247
32
6.3210
3
1.2777
33
32.3888
3
.0555
33
6.7222
4
1.7777
34
34.0000
4
.0988
34
7.1358
5
2.3148
35
35.6481
5
.1543
35
7.5617
6
2.8888
36
37.3333
6
.2222
36
8.0000
7
3.5000
37
39.0555
7
.3025
37
8.4506
8
4.1481
38
40.8148
8
.3951
38
8.9135
9
4.8333
39
42.6111
9
.5000
39
9.3888
10
6.6666
40
44.4444
10
.6173
40
9.8765
11
6.3148
41
46.3148
11
.7469
41
10.3765
12
7.1111
42
48.2222
12
.8889
42
10.8888
13
7.9444
43
50.1666
13
1.0432
43
11.4135
14
8.8148
44
52.1481
14
1.2099
44
11.9506
15
9.7222
46
54.1666
16
1.3889
45
12.5000
16
10.6666
46
66.2222
16
1.5802
46
13.0617
17
11.6481
47
58.3148
17
1.7839
47
13.6358
18
12.6666
48
60.4444
18
2.0000
48
14.2222
19
13.7222
49
62.6111
19
2.2284
49
14.8209
20
14.8148
50
64.8148
20
2.4691
50
15.4321
21
15.9444
51
67.0555
21
2.7222
51
16.0555
22
17.1111
52
69.3333
22
2.9876
52
16.6913
23
18.3148
53
71.6481
23
3.2654
53
17.3395
24
19.5555
54
74.0000
24
3.5555
54
18.0000
25
20.8333
66
76.3888
25
3.8530
66
18.6728
26
22.1481
66
78.8148
26
4.1728
6Q
19.3580
27
23.5000
61
81.2777
27
4.5000
61
20.0555
28
24.8888
58
83.7777
28
4.8395
58
20.7654
29
26.3148
59
86.3148
29
5.1913
59
21.4876
30
27.7777
60
88.8888
30 5.5555
•
60
22.2-222
I
(V.
)
BASE 20— SLOPE li to 1.
Add.
4d
t
.Add.
o •
Deduct.
<4H
"a <
*a S Dedact.
B
31
o*
Q°'
1
.3935
33.7268
1
.0077
31
7.4151
2
.8333
32
36.6566
2
.0309
32
7.9012
3
1.3194
33
37.4305
3
.0694
33
8.4027
4
1.8518
34
39.3518
4
.1234
34
8.9197
5
2.4305
35
41.3194
5
.1928
35
9.4621
6
3.0555
36
43.3333
6
.2778
36
10.0000
7
3.7268
37
45.3935
7
.3781
37
10.5632
8
4.4444
38
47.5000
8
.4938
38
11.1419
9
5.2083
39
49.6527
9
.6250
39
11.7361
10
6.0185
40
51.8518
10
.7716
40
12.3456
11
6.8750
41
54.0972
11
.9336
41
12.9706
12
7.7777
42
56.3888
12
1.1111
42
13.6111
13
8.7268
43
58.7268
13
1.3040
43
14.2680
14
9.7222
44
61.1111
14
1.5123
44
14.9382
15
10.7638
45
63.5416
15
1.7361
45
15.6250
16
11.8518
46
66.0185
16
1.9753
46
16.3271
17
12.9861
47
68.5416
17
2.2299
47
17.0447
18
14.1666
48
71.1111
18
2.5000
48
17.7777
19
15.3935
49
73.7268
19
2.7855
49
18.5262
20
16.6666
50
76.3888
20
3.0864
60
19.2901
21
17.9861
51
79.0972
21
3.4028
51
20.0694
22
19.3518
52
81.8518
22
3.7346
52
20.8641
23
20.7638
53
84.6527
23
4.0818
53
21.6743
24
22.2222
54
87.5000
24
4.4444
54
22.5000
25
23.7268
55
90.3935-
25
4.8228
55
23.3410
26
25.2777
56
93.3333
26
5.2160
56
24.1975
27
26.8750
57
96.3194
27
5.6250
57
25.<694
28
28.5185
58
99.3518
28
6.0494
68 ;25.9567
29
30.2083
59
102.4305
29
6.4891 59
26.8595
30
1 -
31.9444
60
105.5555
30
6.9444 60
27.7777
(iv.)
1
BASE 20 SLOPE 1 to 1.
1
Add.
-a
Add.
4m
Deduct.
<M
Deduct.
1
X
1
K
0*
1
p
1
.3888
31
29.2777
.0062
31
5.9321
1
2
.8148
32
30.8148
2
.«J247
32
6.3210
3
1.2777
33
32.3888
3
.0555
33
6.7222
4
1.7777
34
34.0000
4
.0988
34
7.1358
5
2.3148
35
35.6481
5
.1543
36
7.5617
6
2.8888
36
37.3333
6
.2222
36
8.0000
7
3.5000
37
39.0555
7
.3026
37
8.4506
8
4.1481
38
40.8148
8
.3951
38
8.9135
9
4.8333
39
42.6111
9
.5000
39
9.3888
1
10
5.6665
40
UMU
10
.6173
40
9.8765
11
6.3148
41
46.3148
11
.7469
41
10.3765
12
7.1111
42
48.2222
12
.8889
42
10.8888
13
7.9444
43
50.1666
13
1.0432
43
11.4135
14
8.8148
44
52.1481
14
1.2099
44
11.9506
15
9.7222
45
54.1666
15
1.3889
45
12.5000
16
10.6666
46
66.2222
16
1.5802
46
13.0617
17
11.6481
47
58.3148
17
1.7839
47
13.6358
18
12.6666
48
60.4444
18
2.0000
48
14.2222
19
13.7222
49
62.6111
19
2.2284
49
14.8209
2U
14.8148
50
64.8148
20
2.4691
60
15.4321
21
15.9444
51
67.0555
21
2.7222
51
16.0555
22
17.1111
52
69.3333
22
2.9876
62
16.6913
'
23
18.3148
53
71.6481
23
3.2654
63
17.3395
24
19.5555
54
74.0000
24
3.5555
54
18.0000
25 20.8333
55
76.3888
23
3.8530
55
18.6728
26 22.1481
56
78.8148
26
4.1728
56
19.3580
27 '23.6000
57
81.2777
27
4.5000
57
20.0555
28 24.8888
58
83.7777
28
4.8395
68
20.7054
29 26.3148
59
86.3148
29
5.1913
69
21.1876
30 !27.7777 60
88.8888
30
5.5555
*
60
22.2i22
BASE 20— SLOPE l^ to 1.
**
t
93
Add.
**
1
31
1
.3935
2
.8333
32
3
1.3194
33
4
1.8518
34
5
2.4305
35
6
3.0555
36
7
3.7268
37
8
4.4444
38
9
5.2083
39
10
6.0185
40
11
6.8750
41
12
7.7777
42
13
8.7268
43
14
9.7222
44
15
10.7638
45
16
11.8518
46
17
12.9861
47
18
14.1666
48
19
15.3935
49
20
16.0GG6
50
21
17.9861
61
22
19.3518
52
23
20.7638
53
24
22.2222
54
25
23.7268
55
26
25.2777
56
27
26.8750
57
28
28.5185
58
29
30.2083
59
30
^1.9444
60
Add.
33.7268
35.5555
37.4305
39.3518
41.3194
43.3333
45.3935
47.5000
49.6527
51.8518
54.0972
56.3888
58.7268
61.1111
63.5416
66.0185
68.5416
71.1111
73.7268
76.3888
79.0972
81.8518
84.6527
87.5000
90.3935
93.3333
96.3194
99.3518
102.4305
105.5555
.^5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Dfldaot.
.0077
.0309
.0694
.1234
.1928
.2778
.3781
.4938
.6250
.7716
.9336
1.1111
1.3040
1.5123
1.7361
1.9753
2.2299
2.5000
2.7855
3.0864
3.4028
3.7346
4.0818
4.4444
4.8228
5.2160
5.6250
6.0494
6.4891
6.9444
Dedact.
31
32
33
34
35
86
37
38
39
40
41
42
43
44
45
7.4151
7.9012
8.4027
8.9197
9.4521
10.0000
10.5632
11.1419
11.7361
12.3456
12.9706
13.6111
14.2680
14.9382
15.6250
46 16.3271
47 17.0447
48 '17.7777
49 118.5262
50 19.2901
51 20.0694
52 20.8641
53 21.6743
54 ,22.5000
5o ,23.3410
56 124.1975
57 i25.< 694
58 |25.9567
59 126.8595
60 '27.7777
(vi.
)
BASE 20— SLOPE IJ to 1.
-a
Add.
1
V
Add.
Deduct.
Deduct.
1
»
1
Q*
.3981
31
38.1759
.0092
31
8.8981
2
.8518
32
40.2962
2
.0370
32
9.^815
3
1.3611
33
43.4722
3
.0833
33
10.0833
4
1.9259
34
44.7037
4
.1480
34
10.7037
5
2.5462
35
46.9907
5
.2313
35
11.3425
6
3.2222
36
49.3333
6
.3333
36
12,0000
7
3.9537
37
51.7314
7
.4537
37
12.6759
8
4.7407
38
54.1851
8
.5926
38
13.3703
9
5.5833
39
56.6944
9
.7500
39
14.0833
10
6.4814
40
59.2592
10
.9259
40
14.8148
11
7.4351
41
61.2129
11
1.1203
41
15.5648
12
8.4444
42
64.5555
12
1.3333
42
16.3333
13
9.5092
43
67.2870
13
1.5648
43
17.1202
14
10.6296
44
70.0740
14
1.8148
44
17.9259
15
11.8055
45
72.9166
15
2.0833
45
18.7500
16
13.0370
46
75.8148
16
2.3704
46
19.5925
17
14.3240
47
78.7685
17
2.6759
47
20.4537
18
15.6666
48
81.7777
18
3.0000
48
21.3333
19
17.0648
49
84.8425
19
3.3426
49
22.2314
20
18.5185
50
87.9629
20
3.7037
50
23.1481
21
20.0277
51
91.1388
21
4.0833
51
24.0833
22
21.5925
62
94..3703
22
4.4815
52
25.0370
23
23.2129
53
97.6574
23
4.8981
53
26.0092
24
24.8888
•54
101.0000
24
5.3333
54
27.0000
25
26.6203
55
104.3981
25
5.7869
55
28.0092
26
28.4074
56
107.8518
26
6.2592
56
29.0370
27
30.2500
57
111.3611
27
6.7500
51
30.0833
28
32.1481
58
114.92.59
28
7.2592
58
31.1481
29
34.1018
59
118.5462
29
7.7869
59
32.2314
30
36.1111
60
122.2222
30
8.3333 60
33.3333
J
( 'ii. )
BASE 20— SLOPE IJ to 1.
4J
1
Add.
•s
Add.
S3 33
•
Deduct.
Deduct.
1
X
31
Q*
o*
•
.4027
42.6250
1
.0108
31
10.3811
2
.8703
32
43.0370
2
.0432
32
11.0609
3
1.4027
33
47.5138
3
.0972
33
11.7638
4
2.0000
34
50.0555
4
.1728
34
12.4876
5
2.6620
35
52.6620
6
.2700
36
13.2330
6
3.3888
86
65.3333
6
.3889
36
14.0000
7
4.1805
37
68.0694
7
.5293
37
14.7885
8
6.0370
38
60.8703
8
.6913
38
15.5987
9
6.9683
39
63.7361
9
.8750
39
16.4305
10
6.9444
40
66.6666
10
1.0802
40
17.2839
11
7.9953
41
69.6620
11
1.3071
41
18.1589
12
9.1111
42
72.7222
12
1.5555
42
19.0555
13
10.2916
43
75.8472
13
1.8256
43
19.9747
14
11.6370
44
79.0370
14
2.1173
44
20.9135
16
12.8472
45
82.2916
15
2.4305
45
21 .8750
16
14.2222
46
86.6111
16
2.7654
46
22.8580
17
16.6620
47
8S.9953
17
3.1219
47
23.8626
18
17.1666
48
92.4444
18
3.5000
48
24.8888
19
18.7361
49
95.9583
19
3.8997
49
25.9367
20
20.3703
60
99.6.!f70
20
4.3210
50
27.0061
21
22.0694
61
103.1805
21
4.7639
51
28.0972
22
23.8333
52
106.8888
22
5.2284
62
29.2098
23
26.6620
53
110.6620
23
5.7145
53
30.3441
24
27.6665
54
114.5U00
24
6.2222
64
31.5000
25
29.5138
65
118.4027
25
6.7516
56
32.6774
26
31.6370
56
122.3703
26
7.3024
66
33.8765
27
33.6250
67
126.4027
27
7.8750
57
35.0972
28
35.7777
68
130.6000
28
8.4691
58
36.3394
29
37.9932
69
134.6620
29
9.0848
59
37.6033
30
40.27771 60
138.8888
SO
9.7222
60 38.8888
III. )
(vi
BASE 20— SLOPE 2 to 1.
1
Add.
1
•s
K
31
Add.
Dif. of
-- Hts.
Dedaet.
Dif.of
Hts.
Deduct.
.4074
47.0740
.0123
31
11.8642
2
.8888
32
49.7777
2
.0494
32
12.6419
3
1.4444
33
62.5555 \
3
.1111
33
13.4444
4
2.0740
34
55.4074
4
.1975
34
14.2716
5
2.7777
35
58.3333
5
.3086
35
15.1234
6
3.6555
36
61.3333
6
.4444
36
16.0000
7
4.4074
37
64.4074
7
.6049
37
16.9012
8
5.3333
38
67.5555
8
.7901
38
17.8271
9
6.3333
39
70.7777
9
1.0000
39
18.7777
10
7.4074
40
74.0740
10
1.2346
40
19.7530
11
8,5555
41
77.4444
11
1.4938
41
20.7530
12
9.7777
42
80.8888
12
1.7778
42
21.7777
13
11.0740
43
84.4074
13
2.0864
43
22.8271
14
12.4444
44
88.0000
14
2.4197
44
23.9012
15
13.8888
45
91.6666
16
2.7778
45
25.0000
16
15.4074 i 46
95.4074
16
3.1605
46
26.1234
17
17.0000
47
99.2222
17
3.5679
47
27.2716
18
18.6666
48
103.1111
18
4.0000
48
28.4444
19
20.4074
49
107.0740
19
4.4568
49
29.6420
20
22.2222
50
111.1111
20
4.9382
50
30.8642
21
24.1111
51
115.2222
21
5.4444
51
32.1111
22
26.0740
52
119.4074
22
5.9753
62
33.3827
23
28.1111
53
123.6666
23
6.5309
53
34.6790
24
30.2222
54
128.0000
24
7.1111
54
36.0000
26
32.4074
55
132.4074
25
7.7160
55
37.3456
26
34.6666
56
136.8888
26
8.3457
66
38.7160
27
37.0000
57
141.4444
27
9.0000
67
40.1111
28
39.4074 58
146.0740
28
9.6790
68
41.5308
29
41.8888 , 59
150.7777
29
10.3827
69
42.9753
30 44.4444160
155.6555
130
11.1111 60 144.4444
,. .. ,
.J
(«.)
BASE 20-SLOPE ^ to 1.
t
SB
Add.
1
Add.
3^
Dedvct
^a
§«
Deduct.
T
.4166
31
66.9722
1
.0154
31
148302
2
.9259
32
59.2592
2
.0617
32
15.8016
3
1.5277
33
62.6388
3
.1389
33
m8066
4
2.2222
34
66.1111
4
.2468
34
17.8395
5
a0092
36
69.6769
6
.3857
35
18.9043
6
3.8888
36
73.3333
6
.6656
36
20.0000
7
4.8611
37
77.0833
7
.7561
37
21.1265
8
5.9259
38
80.9269
8
.9876
38
22.2839
9
7.0833
39
84.8611
9
1.2600
39
23.4722
10
8.3333
40
88.8888
10
1.5432
40
24.6913
11
9.6759
41
93.0092
11
1.8673
41
25.9413
12
11.1111
42
97.2222
12
2.2222
42
27.2222
13
12.6388
43
101.5277
13
2.6080
43
28.5360
14
14.2592
44
105.9269
14
3.0247
44
29.8765
16
16.9722
45
110.4166
15
3.4722
46
31.2600
16
17.7777
46
116.0000
16
3.9506
46
32.6643
17
19.6759
47
119.6759
17
4.4599
47
34.0895
18
21.6666
48
124.4444
18
6.0000
48
35.5555
19
23.7500
49
129.3055
19
5.5710
49
37.0524
20
25.9259
50
134.2692
20
6.1728
50
38.5802
21
28.1944
51
139.3055
21
6.8055
61
40.1388
22
30.5555
52
144.4444
22
7.4691
62
41.7283
23
33.0092
53
149.6759
23
8.1636
53
43.3487
24
35.5555
54
155.0000
24
8.8889
54
45.0000
25
38.1944
55
160.4166
25
9.6466
66
46.6820
26
40.9259
56
165.9269
26
10.4321
66
48.3950
27
43.7500
57
171.5277
27
11.2500
57
50.1388
28
46.6666
58
177.2222
28
12.0687
68
51.9136
29
49.6759
59
183.0092
29
12.9782
59
53.7191
30
52.7777
60 188.8888
30
13.8889
60
c
55.5556
( X. )
BASE 20— SLOPE 3 to 1,
•s
Add.
J
Add.
l^
^m
Deduct.
**9
S5B3
1
Deduct.
as
s
1
Q
a
1
.4259
31
64.8703
1
.0186
31
17.7963
2
.9629
32
68.7407
2
.0740
32
18.9630
3
1.6111
33
72.7222
3
.1667
33
20.1666
4
2.3703
34
76.8148
4
.2961
34
21.4074
3
3.2407
35
81.0186
5
.4628
35
22.6851
6
4.2222
36
86.3333
6
.6667
36
24.0000
7
5.3148
37
89.7592
7
.9074
37
25.3618
8
6.5185
38
94.2962
8
1.1852
38
26.7407
9
7.8333
39
98.9444
9
1.5000
39
28.1666
10
9.2692
40
103.7037
10
1.8518
40
29.6296
11
10.7962
41
108.6740
11
2.2407
41
31.i296
12
12.4444
42
113.5655
12
2.6667
42
32.6666
13
14.2037
43
118.6481
13
3.1296
43
34.2405
14
16.0740
44
123.8618
14
3.6296
44
36.8518
15
18.0566
45
129.1666
16
4.1667
45
37.6000
16
20.1481
46
134.5926
16
4.7407
46
39.1851
17
22.3518
47
140.1296
17
5.3518
47
40.9074
18
24.6666
48
145.7777
18
6.0000
48
42.6666
19
27.0925
49
151.6370
19
6.6852
49
44.4629
20
29.6296
60
167.4074
20
7.4074
50
46.2963
21
32.2777
61
163.3888
21
8.1667
61
49.1666
22
35.0370
62
169.4814
22
8.9629
62
50.0740
23
37.9074
53
175.6851
23
9.7962
53
62.0186
24
40.8888
54
182.0000
24
10.6667
54
54.0000
25
-^.9814
65
188.4259
25
f *
11.6741
65
56.0184
26
47.1851
66
194.9629
26
12.5184
56 '58.0640
27
60.6000
57
201.6111
27
13.5000
57 60.1666
28
53.9259
58
206.3703
28
14.6185
58 62.2962
29
57.4629
69
215.2407
29
15.5739
59 64.4629
30
61.1111
60
222.2222
30
16.6667
60 ;66.6666
J
(xi.)
BASE 21— SLOPS
1 1 to 1.
t
X
1
Add.
4J
t
X
Add.
Dif.of
Hts.
Dednct.
Dif.of
Hts.
Deduct.
.3935
31
16.5046
1
.0016
31
1.4830
2
.7962
32
17.1861
2
.00®J
32
1.5802
3
1.2083
33
17.8750
3
.0139
33
1.6805
4
1.6296
34
18.5740
4
.0246
34
1.7839
5
2.0601
35
19.2824
6
.0385
35
1.8904
6
2.5000
36
20.0000
6
.0555
36
2.0000
7
2.9490
37
20.7268
7
.0756
37
2.1126
8
3.4074
38
21.4629
8
.0988
38
2.2284
9
3.8750
39
22.2083
9
.1250
39
2.3472
10
4.3518
40
22.9629
10
.1543
40
2.4691
11
48379
41
23.7268
11
.1867
41
2.6941
12
5.3333
42
24.5000
12
.2222
42
2.7222
13
5.8379
43
26.2824
13
.2608
43
2.8546
14
6.3518
44
26.0740
14
.3025
44
2.9876
16
6.8750
46
26.8750
15
.3472
46
3.1250
16
7.4074
46
27.6851
16
.3951
46
3.2654
17
7.9490
47
28.6046
17
.4460
47
3.4068
18
8.5000
48
29.3333
18
.5000
48
3.6556
19
9.0601
49
30.1712
19
.6571
49
3.7062
20
9.6296
60
31.0186
20
.6173
50
3.8580
21
ia2083
51
31.8760
21
.6805
51
4.0139
22
10.7962
52
32.7407
22
.7469
52
4.1728
23
11.3935
53
33.6157
23
.8163
63
4.33^
24
12.0000
54
34.6000
24
.8889
64
4.5000
25
12.6157
65
35.3935
25
.9647
55
4.6682
26
13.2407
56
36.2962
26
1.0432
66
4.8396
27
13.8750
57
37.2083
27
1.1250
67
5.0139
28
14.5186
58
38.1296
28
1.2099
58
6.1913
29
15.1712
69
39.0601
29
1.2978
59
6.3719
30
15.8333
60
40.0000
30
1.3889
60
5,5665
(xii.)
BASE 21— SLOPE
i to 1.
}
Add.
}
Add.
if. of
Hts.
Dednct.
■5 Eu
Deduct.
1
S
Q
Q
.3981
31
20.9537
1
.0031
31
2.9660
2
.8148
32
21.9259
2
.0123
32
3.1605
3
1.2500
33
22.9166
3
.0278
33
3.6111
4
1.7037
34
23.9259
4
.0494
34
3.5679
5
2.1759
35
24.9537
5
.0772
36
3.7808
6
2.6666
36
26.0000
6
.1111
36
4.0000
7
3.1759
37
27.0648
7
.1512
37
42263
8
3.7037
38
28.1481
8
.1975
38
44568
9
4.2500
39
29.2500
9
.2500
39
46944
10
4.8148
40
30.3703
10
.3086
40
49383
11
5.3981
41
31.5092
11
.3734
41
5.1883
12
6.0000
42
32.6666
12
.4444
42
6.4444
13
6.6203
43
33.8425
13
.5216
43
6.7076
14
7.2592
44
35.0370
14
.6049
44
5.9753
15
7.9166
45
36.2600
15
.6944
46
6.2500
16
8.5925
46
37.4814
16
.7901
46
6.5308
17
9.2870
47
38.7314
17
.8920
47
6.8179
18
10.0000
48
40.0000
18
1.0000
48
7.1111
19
10.7314
49
41.2870
19
1.1142
49
7.4104
20
11.4814
60
42.5925
20
1.2346
50
7.7160
21
12.2500
61
43.9166
21
1.3611
61
8.0277
22
13.0370
52
46.2592
22
1.4938
52
8.3456
23
13.8425
53
46.6203
23
1.6327
53
8.6697
24
14.6666
54
48.0000
24
1.7778
64
9.0000
25
15.5092
55
49.3982
25
1.9295
55
9.3364
26
16.3703
66
60.8148
26
2.0864
56
9.6790
27
17.2500
57
52.2500
27
2.2500
67
10.0277
28
18.1481
58
53.7037
28
2.4197
58
10.3827
29
19.0648
59
55.1769
29
2.5956
59
10.7438
30
20.0000
60
56.6666
30
2.7778
60 11.1111
( xiii. )
BASE 21 SLOPE f to 1.
}
Add.
•8
Add.
if. of
1
Deduct.
Dednct.
«
B
Q
31
1
.4027
31
26.4027
1
.0046
4.4490
2
.8333
32
26.6666
2
.0186
32
4.7407
3
1.2916
33
27.9583
3
.0416
33 5.0416
4
1.7777
34
29.2777
4
.0740
34 5.3518
5
2.2916
35
30.6250
6
.1157
36
6.6712
6
2.8333
36
32.0000
6
.1667
36
aoooo
7
3.4027
37
33.4027
7
.2268
37
&3379
8
4.0000
38
34.8333
8
.2963
38
&6861
9
4.6250
39
36.2916
9
.3750
39
7.0416
10
5.3333
40
37.7777
10 .4630
40
7.4074
11
5.9583
41
39.2916
11 .5602
41
7.7824
12
6.6666
42
40.8333
12
.6667
42
8.1666
13
7.4027
43.
^.4027
13
.7824
43
8.6612
14
8.1666
44
44.0000
14
.9074
44
8.9629
16
8.9583
45
45.6260
15
1.0417
•
45
9.3760
16
9.7777
46
47.2777
16
1.1852
46
9.7962
17
10.6250
47
48.9583
17
1.3379
47
10.2268
18
11.5000
48
50.6666
18
1.6000
48
10.6666
19
12.4027
49
52.4027
19
1.6713
49
11.1167
20
13.3333
50
64.1666
20
1.8618
50
11.6740
21
14.2916
51
55.9583
21
2.0417'
51
12.0416
22
15.2777
52
57.7777
22
2.2407
52
12.6186
23
16.2916
53
69.6250
23
2.4491
63
13.0046
24
17.3333
54
61.5000
24
2.6667
54
13.5000
25
18.4027
55 63.4027
25
2.8935
65
14.0046
26
19.5000
56
65.3333
26
3.1296
56
146186
27
20.6250
57
67.2916
27
3.3760
67
16.0416
28
21.7777
58
69.2777
28
3.6296
68
16.6740
29
22.9583
59
71.2916
29
3.8936
69
16.1157
30
24.1666
60
73.3333
30
4.1667
60
116.6666
( xiv. )
•
BASE 21— SLOPE 1 to 1.
1
V
Add.
■s
Add.
Deduct.
S3 as
Deduct.
1
a
Q
Q
.4074
31
29.8518
1
.0062
31
6.9321
2
.8518
32
31.4074
2
.0247
32
6.3210
3
1.3333
33
33.0000
3
.0555
33
6.7222
4
1.8518
34
34.6296
4
.0988
34
7.1358
5
2.4074
35
36.2962
5
.1543
35
7.6617
6
3.0000
36
38.0000
6
.2222
36
8.0000
7
3.6296
37
39.7407
7
.3025
37
8.4506
8
4.2962
38
41.6185
8
.3951
38
8.9135
9
5.0000
39
43.3333
9
.5000
39
9.3888
10
6.7407
40
45.1861
10
.6173
40
9.8765
11
6.5185
41
47.0740
11
.7469
41
10.3766
12
7.3333
42
49.0000
12
.8889
42
10.8888
13
8.1851
43
60.9629
13
1.0432
43
11.4135
14
9.0740
44
52.9629
14
1.2099
44
11.9606
16
10.0000
45
56.0000
15
1.3889
45
12.5000
16
10.9629
46
67.0740
16
1.5802
46
13.0617
17
11.9629
47
59.1851
17
1.7839
47
13.6358
18
13.0000
48
61.3333
18
2.0000
48
14.2222
19
14.0740
49
63.6185
19
2.2284
49
14.8209
20
15.1851
50
65.7407
20
2.4691
60
15.4321
21
ia3333
51
68.0000
21
2.7222
61
16.a'565
22
17.6186
62
70.2962
22
2.9876
52
16.6913
23
18.7407
53
72.6296
23
3.2654
53
17.3396
24
20.0000
64
76.0000
24
3,5566
64
18.0000
25
21.2962
55
77.4074
25
3.8530
55
18.6728
26
22.6296
56
79.8518
26
4.1728
66
19.3580
27
24.0000
57
82.3333
27
4.5000
57
20.0656
28
26.4074
58
85.8618
28
4.8395
58
20.7654
29
26.8518 69
87.4074
29
5.1913
69
21.4876
30
28.3333 60
90.0000
30
5.5666 60
22.2222
(XV
•)
1
■ 1
BASE 21 SLOPE
li to 1.
t
Add.
1
X
Add.
° a
ran
a
1
Deduct.
31
1
Deduct.
1
1
.4120
31
34.3009
.0077
7.4161
2
.8703
32
36.1481
2
.0309
32
7.9012
3
1.3750
33
38.0416
3
.0^4
33
8.4027
4
1.9259
34
39.9814
4
.1234
34
8.9197
5
2.5231
35
41.9675
5
.1928
35
9.4521 I
6
3.1666
36
44.0000
6
.2778
36
10.0000
7
3.8564
37
46.0787
7
.3781
37
10.5632 1
8
4.5925
38
48.2037
8
.4938
38
11.1419 ;
9
5.3750
39
50.3750
9
.6250
39
11.7361 1
10
6,2037
40
52.5925
10
.7716
40
12.3456
11
7.0787
41
54.8564
11
.9336
41
12.9706
12
8.0000
42
57.1666
12
1.1111
42
13.6111
13
8.9675
43
59.5231
13
1.3040
43
14.2680
14
9.9814
44
61.9259
14
1.5123
44
14.9382
15
11.0416
45
64.3750
15
1.7361
45
15.6250
16
12.1481
46
66.8703
16
1.9753
46
16.3271
17
13.3009
47
69.4120
17
2.2299
47
17.0447
18
14.5000
48
72.0000
18
2.5000
48
17.7777
19
15.7453
49
74.6342
19
2.7856
49
18.6262
20
17.0370
50
77.3148
20
3.0864
50
19.2901
21
18.3750
61
80.0416
21
3.4028
51
20.0694
22
19.7592
52
82.8148
22
3.7346
52
20.8641
23
21.1898
53
86.6342
23
4.0818
63
21.6743
24
22.6666
54
88.6000
24
4.4444
54
22.6000
25
24.1898
55
91.4120
25
4.8228
55
23.3410
26
25.7592
56
94.3703
26
6.2160
66
24.1976
27
27.3750
57
97.3750
27
6.6250
67
25.0694
28
29.0370
58
100.4259
28
6.0494
58
25.9567
29
30.7453
59
103.5231
29
6.4891
59
26.8696
30
32.5000
60
106.6666
30
6.9444
60
•
27.7777
" '
(xtL)
BASE 21— SLOPE IJ to 1.
1
Add.
Add.
Deduct.
if. of
Ht8.
Deduct.
m
X
Q
Q
1
.4166
31
38.7500
1
.0092
31
8.8981
2
.8888
32
40.8888
2
.0370
32
9.4815
3
1.4166
33
43.0833
3
.0833
33
10.0833
4
2.0000
34
45.3333
4
.1480
34
10.7037
5
2.6388
35
47.6388
5
.2313
36
11.3^25
6
3.3333
36
50.0000
6
.3333
36
12.0000
7
4.0833
37
52.4166
7
.4537
37
12.6759
8
4.8888
38
54.8888
8
.5926
38
13.3703
9
5.7500
39
67.4166
9
.7500
39
14.0833
10
6.6666
40
60.0000
10
.9259
40
148148
11
7.6388
41
62.6388
11
1.1203
41
16.5648
12
8.6666
42
65.3333
12
1.3333
42
16.3333
13
9.7500
43
68.0833
13
1.5648
43
17.1202
14
10.8888
44
70.8888
14
1.8148
44
17.9259
15
12.0833
45
73.7500
16
2.0833
45
18.7500
16
13.3333
46
76.6666
16
2.3704
46
19.6926
17
14.6388
47
79.6388
17
2.6759
47
20.4537
18
16.0000
48
82.6666
18
3.0000
48
21.3333
19
17.4166
49
85.7500
19
3.3426
49
22.2314
20
18.8888
50
88.8888
20
3.7037
50
23.1481
21
20.4166
51
92.0833
21
40833
61
24.0833
22
22.0000
52
95.3333
22
4.4815
62
26.0370
23
23.6388
53
98.6388
23
48981
53
26.0092
24
25.3333
54
102.0000
24
6.3333
64
27.0000
25
27.0833
55
105.4166
26
5.7869
55
28.0092
26
28.8888
56
108.8888
26
6.2592
56
29.0370
27
30.7500
57
112.4166
27
6,7500
67
30.0833
28
32.6666
58
116.0000
28
7.2592
58
31.1481
29
34.6388
59
119.6388
29
7.7869
69
32.2314
30
36.6666
•
60
123.3333
30
8.3333
60
33.3333
J
( xvii. )
BASE 21--SL0PE If to 1.
}
Add.
A4d.
•
Deduct.
|s
Deduct.
ffl
H
1
1
.4212
31
43.1990
.0108
31
10.3811
2
.9074
32
45.6296
2
.0432
32
11.0609
8
1.4583
33
48.1250
8
.0972
83
11.7688
4
2.0740
34
60.6851
4
.1728
84
12.4876
5
2.7546
85
53.8101
5
.2700
85
18.2330
6
3.6000
86
56.0000
6
.3889
86
14.0000
7
4.3101
37
68.7546
7
.5293
37
14.7885
8
6.1851
88
61.5740
8
.6913
38
15.6987
9
6.1280
39
64.4683
9
.8760
39
16.4306
10
7.1296
46
67.4074
10
1.0802
40
17.2839
11
8.1990
41
70.4212
11
1.3071
41
18.1589
12
9.3338
42
73.6000
12
1.5555
42
19.0555
13
10.6324
43
76.6435
18
1.8256
48
19.9747
14
11.79^
44
79.8618
14
2.1173
44
20.9136
16
18.1250
46
83.1260
16
2.4305
45
21.8760
16
14.5185
46
86.4629
16
2.7664
46
22.8580
17
16.9768
47
89.8657
17
3.1219
47
23.8626
18
17.6000
48
93.3333
18
3.6000
48
24.8888
19
19.0879
49
96.8657
19
3.8997
49
25.9367
20
20.7407
60
100.4629
20
4.3210
60
27.0061
61
22.4583
51
104.1250
21
4.7639
51
28.0972
22
24.2407
62
107.8518
22
6.^84
52
29.2098
23
26.0879
53
111.6435
23
5.7145
63
30.3441
24
28.0000
64
116.6000
24
6.2222
54
31.6000
25
29.9768
55
119.4212
25
6.7516
66
32.6774
26
82.0186
56
123.4074
26
7.3024
56
88.8765
27
841260
57
127.4683
27
7.8760
57
35.0972
28
36.2962
58
131.6740
28
8.4691
58
36.3394
29
38.6324
59
135.7546
29
9.0848
59
37.6038
30
40.8338
60
140.0000
30
9.7222
60
D
38.8888
( xriii. )
BASE 21— SLOPE 2 to 1.
1
Add.
1
Add.
"a
Deduct.
Dedoct.
1
»
a
Q
.4259
31
47.6481
1
.0123
31
11.8642
2
.9259
32
60.3703
2
.0494
32
12.6419
3
1.5000
33
63.1666
3
.1111
33
13.4444
4
2.1481
34
56.0370
4
.1975
34
14.2716
5
2.8703
36
68.9814
6
.3086
36
16.1234
6
3.6666
36
62.0000
6
.4444
36
16.0000
7
46370
37
65.0925
7
.6049
37
16.9012
8
5.4814
38
68.2692
8
.7901
38
17.8271
9
6.6000
39
71.6000
9
1.0000
39
18.7777
10
7.5925
40
748148
10
1.2346
40
19.7590
11
8.7692
41
78.2037
11
1.4938
41
20.7630
12
10.0000
*2
81.6666
12
1.7778
42
21.7777
13
11.3148
43
85.2037
13
2.0864
43
22.8271
14
12.7037
44
88.8148
14
2.4197
44
23.9012
15
14.1666
46
92.5000
16
2.7778
45
26.0000
16
15.7037
46
96.2592
16
3.1606
46
26.1234
17
17.3148
47
100.0925
17
3.6679
47
27.2716
18
19.0000
48
104.0000
18
40000
48
28.4444
19
20.7692
49
107.9814
19
44568
49
29.6420
20
22.5928
60
112.0870
20
49382
50
30.8642
21
246000
61
116.1666
21
6.4444
61
32.1111
22
26.4814
62
120.3703
22
5.9753
62
33.3827
23
28.5370
53
1246481
23
6.5309
63
34.6790
24
30.6666
64
129.0000
24
7.1111
64
36.0000
25
32.8703
55
133.4259
25
7.7160
66
37.3466
26
35.1481
56
137.9269
26
8.3467
66
38.7160
27
37.6000
67
142.5000
27
9.0000
67
40.1111
28
39.9259
58
147.1481
28
9.6790
68
41.6308
29
42.^69
69
151.8703
29
10.3827
59
42.9763
30
46.0000
4
60
156.6666
30
11.1111 60
44.4444
-
( xix. )
BASE 21 SLOPE ^ to 1.
t
A4d.
1
Add.
Dif.of
Deduct.
Dif.of
Ht(.
Deduct.
1
.4351
31
56.5462
1
.0154
31
148302
2
.9^9
32
59.8518
2
.0617
32
16.8018
3
1.5833
33
63.2500
3
.1389
33
1&8055
4
2.2962
34
66.7407
4
.2468
34
17.8896
5
aioi8
35
70.3240
5
.3857
36
18.9043
6
40000
36
740000
6
.6666
36
20.0000
7
49907
37
77.7685
7
.7561
37
21.1265
8
6X)740
38
81.6296
8
.9876
38
22.2839
9
7.2500
39
85.5833
9
1.2600
39
23.4722
10
a5185
40
89.6296
10
1.6432
40
24.6913
11
9.8796
41
98.7685
11
1.8673
41
26.9413
12
11.2962
42
98.0000
12
2.2222
42
27.22J^
13
12.8796
43
102.3240
13
.2.6080
43
2a6360
14
14.5185
44
106.7407
14
3.0247
44
29.8765
IS
1&2500
45
111.2500
15
3.4722
45
81.2600
16
18.0740
46
115.8618
16
3.9606
46
32.6543
17
19.9907
47
120.546i
17
44699
47
84.0895
18
22.0000
48
125.3333
18
5.0000
48
35.5566
19
241018
49
130.2129
19
6.6710
49
37.0624
20
26.2962
50
135.1861
20
6.1728
50
38..5802
21
28.5833
51
140.2600
21
6.8065
51
40.1388
22
30.9629
52
146.4074
22
7.4691
52
41.7283
23
33.4351
53
160.6674
23
8.1636
53
43.8487
24
36.0000
54
156.0000
24
8.8889
54
46.0000
25
88.6574
65
161.4361
25
9.6466
65
46.6820
26
41.4074
56
166.9629
26
10.4821
66
48.3960
27
442500
67
172.6833
27
11.2500
57
50.1388
28
47.1851
58
178.2962
28
12.0587
58
51.9135
29
50.2129
59
1841018
29
12.9782
59
53.7191
30
63.3333
60
190.0000
30
13.8889
60
66.5565
(zx.)
BASE 21— SLOPE 3 to 1.
»
1
2
3
4
&
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Add.
AAAA
• X J. X X
1.0000
1.6666
2.4444
a333d
4.SS33
5.4444
6.6666
8.0000
9.4444
ll.OOOQ
12.6666
UA4A4
• XX X X
16.3333
18.3333
20.4444
22.6666
25.0000
27.4444
30.0000
32.6666
35.4444
38.3333
41.3333
44.4444
47.6666
51.0000
54.4444
58.0000
61.6666
31
32
33
34
35
36
37
38
39
4&
41
42
43
44
45
46
47
48^
49
50
51
52
53
54
55
56
57
58
59
60
Add.
65.4444
69.3333
73;3333
77.4444
81.6666
86.0000
90.4444
95.0000
99.6666
104.4444
109.3333
114.3333
119.4444
124.6666
130.0000
135.4444
141.0000
146.6666
130.0000
135.4444
141.0000
146.6666
152.4444
158.3333
164.3333
170.4444
202.6666
209.4444
216.3333
223.3333
1
2
3
4
6
Deduct.
.0185
.0740
.1667
.2961
.4628
".a
g
Deduct.
6
.6667
7
.9074
8
1.1852
1.5000
10
1.8518
11
2.2407
12
2.6667
13
3.129&
14
3.6296
16
4.1667
16
4.7407
17
5.3516
18
6.0000^
1»
a6852
20
7.4074
21
8.1667
22
8.9629
23
9.7962
24
10.6667
25
11.5741
26
12.5184
27
13.5000
28
14.5185
29
15.5739
30
16.6667
m 17.7963
32 18.9630
33 20.1666
34 21.4074
35 22.6851
36 24.0000
37 25.3518
38 26.7407
39 28.1666
40 29.6296
41 31.1296
42 32.6666
43 34.2405
44 35.8518
45 37.5000
46 39.1851
47 40.9074
48 42.6666
49 44.4629
50 46.2963
51 49.166ft
52 60.0740
53 52.0185
54 54.0000
55 56.0184
m 58.0640
57 60.1666
58 62.2962
59 64.4629
60 66.666ft
;
(ixi.)
BASE 22— SLOPE i to 1.
^ 1
\ a
Add.
i
a
31
Add.
ga
1
Deduct.
2^
ga
31
Deduct,
1
1
.4120
17.0787
.0016
1.4830
2
.8333
82
17.7777
2
.0062
82
1.5802
3
1.2638
83
18.4861
3
.0139
33
1.6805
4
1.7037
34
19.2087
4
.0246
34
1.7839
5
2.1627
85
19.9305
6
.0385
36
1.8904
6
2.6111
36
20.6666
6
.0565
86
2.0000
7
3.0787
37
21.4120
7
.0766
87
2.1126
8
3.5555
38
22.1666
8
.0988
38
2.2284
9
40416
89
22.9306
9
.1260
39
2.8472
10
4.5370
40
28.7037
10
.1643
40
2.4691
11
5.0416
41
24.4861
11
.1867
41
2.5941
12
5.5555
42
26.2777
12
.2222
42
2.7222
13
6.0787
43
26.0787
18
.2608
48
2.8646
14
6.6111
44
26.8888
14
.3026
44
2.9876
15
7.1527
45
27.7088
15
.8472
45
3.1260
16
7.7087
46
28.6870
16
.3961
46
8.2654
17
8.2638
47
29.8760
17
.4460
47
3.4089
18
8.8333
48
30.2222
18
.5000
48
3.5555
19
9.4120
49
31.0787
19
.6671
49
3.7052
20
10.0000
60
31.9444
20
.6173
60
3.8580
21
10.5972
51
32.8194
21
.6806
61
4.0139
22
11.2037
52
83.7037
22
.7469
62
4.1728
23
11.8194
58
84.5972
23
.8163
53
4.3349
24
12.4444
54
35.5000
24
.8889
64
4.6000
25
13.0787
55
36.4120
25
.9647
65
4.6682
26
13.7222
66
37.3333
26
1.0432
66
4.8396
27
14.3750
67
38.2638
27
1.1250
67
5.0189
28
16.0370
58
39.2037
28
1.2099
58
6.1913
29
15.7088
59
40.1527
29
1.2978
69
6.3719
30
16.3888 60
41.1111
30
1.3889
60
5.5665
( ""• )
BASE 22— SLOPE J to 1. |
1
a
1
Add.
1
a
Add.
Dif. of
Utf.
Deduct.
Dif. of
Hts.
Dedoot.
.4166
31
21.5277
1
.0031
31
2.9680
2
.8518
32
22.6185
2
.0123
32
3.1605
3
1.3055
33
23.6277
3
.0278
33
36111
4
1.7777
34
24.5555
4
.0494
34
3.5679
6
2.2685
35
26.6018
5
.0772
36
3.7808
6
2.7777
36
26.6666
6
.1111
36
4.0000
7
3.3055
37
27.7600
7
.1512
37
4.2263
8
3.8518
38
28.8518
8
.1976
38
4.4668
9
4.4166
39
29.9722
9
.2500
39
4.6944
10
6.0000
40
31.1111
10
.3086
40
4.9383
11
5.6018
41
32.2686
11
.3734
41
5.1883
12
6.2222
42
33.4444
12
.4444
42
5.4444
13
6.8611
43
34.6388
13
.5216
43
5.7067
14
7.5185
44
35.8618
14
.6049
44
5.9753
16
8.1944
45
37.0833
15
.6944
45
6.2500
16
8.8888
46
38.3333
16
.7901
46
6.5308
17
9.6018
47
39.6018
17
.8920
47
6.8179
18
10.3333
48
40.8888
18
1.0000
48
7.1111
19
11.0833
49
42.1944
19
1.1142
49
7.4104
20
11.8518
50
43.6185
20
1.2346
50
7.7160
21
12.6388
51
44.8611
21
1.3611
51
8.0277
22
13.4444
52
46.2222
22
1.4938
62
8.3456
23
14.2685
53
47.6018
23
1.6327
63
8.6697
24
15.1111
54
49.0000
24
1.7778
54
9.0000
25
15.9722
55
50.4166
25
1.9296
65
9.3364
26
16.8518
56
61.8518
26
2.0864
66
9.6790
27
17.7500
57
63.3055
27
2.2500
57
10.0277
28
18.6666
58
64.7777
28
2.4197
58
10.3827
29
19.6018
59
66.2685
29
2.6956
59
10.7438
30 20.55551
60
67.7777
30
2.7778
60
11.1111
J
( xxiii. )
BASE 22— SLOPE | to 1.
•a
•s
Add.
<fc»
Add.
mi
Deduct.
Deduct.
as
a
1
Q*"
1
.42r2
31
26.9768
.0046
31
4.4490
2
.8703
32
27.2592
2
.0186
32
4.7407
3
1.3472
33
28.5694
3
.0416
33
5.0416
4
1.8618
34
29.9074
4
.0740
34
5.3518
5
2.3842
36
31.2731
6
.1167
36
66712
6
2.9444
36
32.6666
6
.1667
36
6.0000
7
3.6324
37
34.0879
7
.2268
37
63379
8
4.1481
38
36.6370
8
.2963
38
6.6851
9
4.7916
39
37.0138
9
.3750
39
7.0416
10
6.4629
40
38.6186
10
.4630
40
7.4074
11
6.1620
41
40.0609
11
.5602
41
7.7824
12
6.8888
42
41.6111
12
.6667
42
8.1666
13
7.6436
43
43.1990
13
.7824
43
8.5612
14
8.4269
44
44.8148
14
.9074
44
89629
15
9.2361
46
46.4583
16
1.0417
45
9.3750
16
10.0740
46
48.1296
16
1.1852
46
9.7962
17
10.9398
47
49.8287
17
1.3379
47
10.2268
18
11.8333
48
51.6555
18
1.5000
48
10.6666
19
12.7509
49
63.3101
19
1.6713
49
11.1167
20
13.7037
50
56.0925
20
1.8518
60
11.6740
21
14.6806
61
66.9027
21
2.0417
51
12.0416
22
16.6851
62
58.7407
22
2.2407
62
12.6186
32
16.7175
63
60.6064
23
2.4491
63
13.0046
24
17.7777
54
62.6000
24
2.6667
64
13.5000
26
ia8667
55
64.4212
26
2.8936
66
14.0046
26
19.9814
66
66.3703
26
3.1296
56
14.5185
27
21.1260
67
68.3472
27
3.3760
67
15.0416
28
$^.2962
68
70.3518
28
3.6296
68
15.6740
29
23.^63
69
72.3842
29
3.8936
59
16.1157
30
24.7222
60
74.4444
30
4.1667
60
1&6666
( xxiv. )
BASE 22— SLOPE 1 to 1. f|
i
Add.
1
Add.
Deduct,
Deduct.
»
X
1
o
;
1
.4259
31
30.4269
.0062
3i
5.9321
2
.8888
32
32.0000
2
.0247
32
6.3210 •
3
1.3888
33
33.6111
3
.0656
33
6.7222 :
4
1.9259
34
36.2692
4
.0988
34
7.1358 i
5
2.5000
36
36.9444
6
.1643
36
7.6617
6
3.1111
36
38.6666
6
.2222
36
8.0000
7
3.7692
37
40.^69
7
.3026
37
8.4506 ;
8
4.4444
38
42.2222
e
.3951
38
8.9136 '
9
5.1666
89
44.0655
9
.5000
39
9.3888
10
5.9259
40
45.9259
10
.6173
40
9.8766
11
6.7222
41
47.8333
11
.7469
41
10.3765
12
7.5555
42
49.7777
12
.8889
42
10.8888
13
8.4259
43
51.7692
13
1.0432
43
11.4136
1
14
9.3333
44
53.7777
14
1.2099
44
11.9506
15
10.2777
45
65.8333
15
1.3889
46
12.5000
16
11.2592
46
67.9269
16
1.5802
46
13.0617
17
12.2777
47
60.0556
17
1.7839
47
13.6358
18
13.3333
48
62.2222
18
2.0000
48
14.2222
19
14.4259
49
64.4959
19
2.2284
49
14.8209
20
15.5555
50
66.6666
20
2.4691
60
15.4321
21
16.7222
51
68.9444
21
2.7222
61
16.0556
22
17.9259
52
71.2592
22
2.9876
52
16.6913
23
19.1666
53
73.6111
23
3.2654
63
17.3396
24
20.4444
64
76.0000
24
3.5555
64
18.0000
25
21.7692
56
78.4269
25
3.8530
55
18.6728
26
2ailll
56
80.8888
26
4.1728
56
19.3580
27
24.6000
57
83.3888
27
4.6000
57
20.0655
28
25.9269
58
«6.9259
28
4.8395
58
20.7654
29
27.3888
69
88.6000
29
5.1913
69
21.4876 i
30
28.8888
60
91.1111
30
6.5565
60
22.2222
- «
.- , - ■ '
( ^*^* )
BASE 22— SLOPE IJ to 1.
■g,
%
Add.
1
Add.
s
ti m Deduct.
O •
Sednct.
X
1
»
Q'^
o*
.4305
31
34.8760
I
.0077
31
.7.4151
2
.9074
32
36.7407
2
.0309
32
7.9012
3
1.4305
33
38.6527
3
.0694
33
8.4027
4
2.0000
34
40.6111
4
.1234
34
8.9197
5
2.6167
35
42.6167
6
.1928
36
d.4521
6
3.2777
36
44.6666
6
.2778
36
laoooo
7
3.9861
37
46.7638
7
.3781
37
10.5632
«
4.7407
38
48.9074
8
.4938
38
11.1419
9
6.6416
39
51.0972
9
.6250
39
11.7361
10
&3888
40
63.3333
10
.7716
40
12.3456
11
7.2824
41
65.6167
11
.9336
41
12.9706
12
8.2222
42
57.9444
12
1.1111
42
13.6111
13
9.2083
43
60.3194
13
1.3040
43
14.2680
14
10.2407
44
62.7407
14
1.6123
44
149382
15
11.3194
45
66.2083
16
1.7361
45
15.6260
16
12.4444
46
67.7222
16
1.9763
46
16.3271
17
13.6157
47
70.2824
17
2.2299
47
17.0447
18
14.8333
48
72.8888
18
2.5000
48
17.7777
19
16.0972
49
75.6416
19
2.7865
49
18.5262
20
17.4074
60
78.2407
20
3.0864
60
19.2901
21
18.7638
51
80.9861
21
a4028
61
20.0694
22
20.1666
52
83.7777
22
3.7346
52
20.8641
23
21.6167
63
86.6167
23
4.0818
53
21.6743
24
23.1111
64
89.5000
24
4.4444
54
22.6000
26
24.6527
56
92.4306
2S
4.8228
65
23.3410
26
26.2407
66
95.4074
26
5.2160
66
24.1976
27
27.8750
57
98.4305
27
5.6250
57
26.ce94
28
29:5655
58
101.6000
28
6.0494
68
25;9567
29
31.2824
59
104.6157
29
6.4891
69
26.8595
30
3a0566
60
107.7777
30 6.94441
60
E
iW.7777
( xxvi. )
BASE 22-8LOPE IJ to 1.
1
1
Add.
1
Add.
Deduct.
Deduct.
ffi
a
1
o*"
1
.4351
31
39.3240
.0092
31
8.8981
2
.9259
32
41.4814
2
.0370
32
9.4816
8
1.4722
33
43.6944
3
.0633
33
10.0833
4
2.0740
34
46.9629
4
.1480
34
10.7037
6
2.7314
35
48.2870
6
.2313
35
11.3436
6
3.4444
36
50.6666
6
.3333
36
12.0000
7
42129
37
53.1018
7
.4537
37
12.6759
8
5.0370
38
66.5925
8
.5926
38
13.3708
9
5.9166
39
68.1388
9
.7500
89
14.0833
10
a851R
40
60.7407
10
.9259
40
14.8148
11
7.8425
41
63.3081
11
1.1203
41
15.6648
12
8.8888
4a,
66.1111
12
1.3333
42
16.3833
13
9.9907
43
68.8796
13
1.5648
48
17.1202
14
11.1481
44
71.7037
14
1.8148
44
17.9269
15
12.8611
45
74.5833
15
2.0833
45
18.7600
16
13.6296
46
77.6186
16
2.3704
46
19.5926
17
14.9537
47
80.5092
17
2.6769
47
20.4637
18
1&3333
48
83.5566
18
3.0000
48
21.3333
19
17.7685
49
86.6674
19
3.3426
49
22.2314
20
19.2592
50
89.8148
20
3.7037
60
23.1481
21
20.8055
61
93.0277
21
4.0833
51
24.0833
22
22.4074
52
96.2962
22
4.4816
62
25.0870
23
24.0648
53
99.6203
23
4.8981
53
26.0092
24
25.7777
64
103.0000
24
6.3333
64
27.0000
25
27.6462
55
106.4361
25
5.7869
65
28.0092
26
29.3703
66
109.9269
26
6.2692
56
29.0370
27
31.2600
57
113.4722
27
6.7600
67
3J.0833
28
33.1861
58
117.0740
28
7.2692
68
31.1481
29
36.1759 69
120.7314
29
7.7869
69 32.2314 1
30
37.2222 60
124.4444
30
8.3333 60 33.3333
( xxTii. )
BASE 22— SLOPE If to 1.
•a,
•s
Add.
i
Add.
Deduct.
•a
Dednet.
!S
X
31
& >*♦
Q*
1
.4398
43.7731
1
.0108
81
10.3811
2
.9444
32
46.2222
2
.0432
82
11.0609
8
1.5138
33
48.7361
3
.0972
88
11.7638
4
2.1481
34
61.3148
4
.1728
34
12.4876
6
2.8472
36
53.9583
5
.2700
36
13.2330
6
3.6111
36
66.6666
6
.3889
86
140000
7
4.4398
37
69.4398
7
.5293
87
147886
8
5.3333
38
62.2777
8
.6913
38
16.5987
9
6.2916
39
65.1805
9
.8750
39
16.43(»5
10
7.3148
40
68.1481
10
1.0802
40
17.2839
11
8.4027
41
71.1805
11
1.3071
41
18.1689
12
9.5556
42
74.2777
12
1.6666
42
19.0555
13
10.7731
43
77.4398
13
1.8266
43
19.9747
14
12.0565
44
80.6666
14
2.1173
44
20.9136
15
13.4027
46
83.9683
16
2.4a06
45
21.8750
16
148148
46
87.3148
16
2.7654
46
22.8680
17
16.2916
47
90.7361
17
3.1219
47
28.8626
18
17.8333
48
94.2222
18
3.5000
48
24.8888
19
19.4398
49
97.7731
19
8.8997
49
26.93(»7
20
21.1111
50
101.3888
20
43210
60
27.0061
21
22.8472
61
105.0694
21
47639
51
28.0972
22
24.6481
52
108.8148
22
5.2284
62
29.2098
i3
26.6137
53
112.6260
23
6.7146
53
30.3441
24
28.4444
54
116.5000
24
6.2222
64
31.6000
26
30.4398
56
120.4398
25
6.7516
55
32.6774
26
32.6000
56
124.4444
26
7.3024
56
83.8766
27
846250
57
128.5138
27
7.8750
57
35.0972
28
36.8148
58
132.6481
28
8.4691
68
36.3394
29
39.0694
69
136.8472
29
9.0848
69
37.6033
SO
41.8888
60
141.1111
30
9.7222
60
88.8888
( xxviii. )
.
BASE 22 SLOPE 2 to 1.
4^
Add.
1
Add.
if. of
Deduct.
° s
■SB' Deduct.
•
n
1
X
31
1
P"^
AAA4
• Jl X X X
48.2222
.0123
31
11.8642
2
.9629
32
60.9629
2
.0494
32
12.6419
'
3
1.6666
33
63.7777
3
.1111
33
13.4444
4
2.2222
34
66.6666
4
.1976
34
14.2716
5
2.9629
36
69.6296
6
.3086
36
15.1234
6
3.7777
36
62.6666
6
AAAA
• M X'X'X
36
16.0000
7
4.6666
37
66.7777
7
.6049
37
16.9012
, 8
6.6296
38
68.9629
8
.7901
38
17.8271
9
6.6666
39
72.2222
9
1.0000
39
18.7777
10
7.7777
40
76.6566
10
1.2346
40
19.7630
11
8.9629
41
78.9629
11
1.4938
41
20.7530
12
10.2222
42
82.4444
12
1.7778
42
21.7777
13
11.6666
43
86.0000
13
2.0864
43
22.8271
14
12.9629
41
89.6296
14
2.4197
44
23.9012
16
14.4444
46
93.3333
16
2.7778
46
26.0000
16
16.0000
46
97.1111
16
3.1605
46
26.1234
17
17.6296
47
100.9629
17
3.6679
47
27.2716
18
19.3333
48
104.8888
18
4.0000
48
28.4444
19
21.1111
49
108.8888
19
4.4668
49
29.6420
20
22.9629
60
112.9629
20
4.9382
60
80.8642
21
24.8888
61
117.1111
21
6.4444
51
32.1111
: 22
26.8888
62
121.3333
22
6.9753
52
33.3827
23
28.9629
63
126.6296
23
6.6309
53
34.6790
24
31.1111
64
130.0000
24
7.1111
64
36.0000
9
26
33.3333
66
134.4444
26
7,7160
56
37.3466
26
36.6296
66
138.9629
26
8.3467
56
38.7160
27
38.0000
67
143.6666
27
9.0000
67
40.1111
28
40.4444
68
148.2222
28
9.6790
68
41.5308
29
42.9629
69
162.9629
29
10.3827
69
42.9753
30
46.66661 60 1 167.7777
30
11.1111
60 '44.4444
r.
( xxix. )
BASE 22— SLOPE 2J to 1.
•4J
•a.
t
■Si
'Sa
•s
Add.
•s
Add.
»3ffi
Deduct.
;ss
Dedoct.
X
!S
Q
Q
1
.4536
31
57.1203
1
.0164
31
14.8302
2
1.000«>
32
60.4444
2
.0617
32
15.8015
3
1.6388
33
63.8611
3
.1389
33
16.8055
4
2.3704
34
67.3703
4
.2468
34
17.8395
5
3.1944
35
70.9722
6
.3867
36
18.9043
6
4.1111
36
74.6666
6
.5566
36
20.0000
7
5.1202
37
78.4637
7
.7561
37
21.1265
8
6.2222
38
82.3333
8
.9876
38
22.2839
9
7.4166
39
86.3055
9
1.2600
39
23.4722
10
8.7036
40
90.3704
10
1.6432
40
24.6913
11
10.0833
41
94.5277
11
1.8873
41
25.9413
12
11.6556
42
98.7777
12
9.2222
42
27.2222
13
13.1203
43
103.1203
13
2.6080
43
28.6360
14
14.7777
44
107.6665
14
3.0247
44
29.8765
15
17.6278
45
112.0633
16
3.4722
46
31.2600
16
18.3704
46
116.7037
16
3.9506
46
32.6643
17
20.3055
47
121.4166
17
4.4599
47
34.0895
18
22.3338
48
126.2222
18
5.0000
48
36.6656
19
24.4537
49
131.1203
19
6.6710
49
37.0624
20
26.6666
50
136.1111
20
6.1728
50
38.6802
21
28.9722
61
141.1944
21
6.8066
61
40.1388
22
31.3703
62
146.3703
22
7.4691
62
41.7283
23
33.8611
53
151.6388
23
8.1636
63
43.3487
24
36.4444
54
167.0000
24
8.8889
64
45.0000
25
39.1203
65
162.4536
26
9.6465
66
46.6820
26
41.8888
56
168.0000
26
10.4321
66
48.3950
27
44.7500
67
174.6389
27
11.2600
57
50.1388
28
47.7036
58
179.3703
28
12.0587
58
51.9135
29
60.7600
59
186.1944
29
12.9782
59
53.7191
30
53.8888
60
191.1111
30
13.8889
60
55.5655
■1
(xxx.)
BASE 22— SLOPE 3 to 1.
Add.
1
a
Add.
Dif.of
Bti.
Deduct.
Dif.of
Hts.
Deduct.
1
.4628
31
66.0185
1
.0186
31
17.7963
2
1.0370
32
69.9259
2
.0740
32
18.9630
3
1.7222
33
73.9444
3
.1667
33
20.1666
4
2.6185
34
78.0740
4
.2961
34
21.4074
5
3.^59
35
82.3148
6
.4628
36
22.6851
6
44444
36
8&6666
6
.6667
36
240000
7
5.6740
37
91.1296
7
.9074
37
25.3618
8
6.8148
38
95.7037
8
1.1862
38
26.7407
9
8.1666
39
100.3888
9
1.5000
39
28.1666
10
9.6296
40
106.1852
10
1.8518
40
29.6296
11
11.2037
41
110.0926
11
2.2407
41
31.1296
12
12.8888
42
115.1111
12
2.6667
^
32.6666
13
14.6852
43
120.2407
13
3.1296
43
34.2405
14
1&5925
44
125.4813
14
3.6296
44
35.8518
15
19.6111
45
130.8333
16
4.1667
45
37.5000
16
20.7407
46
136.2962
16
4.7407
46
39.1861
17
1^2.9813
47
141.8702
17
6.3518
47
40.9074
18
25.3333
48
147.5656
18
6.0000
48
42.6666
19
27.7962
49
163.3518
19
6.6862
49
44.4^29
20
30.3703
50
159.2593
20
7.4074
50
46.2963
21
33.0555
51
165.2777
21
8.1667
61
49.1666
22
35.8518
62
171.4073
22
8.9629
62
50.0740
23
38.7592
63
177.6480
23
9.79®2
53
62.0185
24
41.7777
54'
184.0000
24
10.6667
64
640000
25
44.9073
55
190.4628
25
11.5741
55
66.0184
26
48.1480
56
197.0370
26
12.5184
56
58.0640
27
51.5000
57
204.7222
27
13.5000
57
60.1666
28
54.9628
58
210.5185
28
145186
58
62.2962
29
68.5370
59
217.4258
29
15.6739
69
644629
30
62.2222
60
224.4444
30
16.6667
60
66.6666
( xxxi. )
BASE 23— SLOPE J to 1.
1
n
Add.
1
n
Add.
Dif. of
Hts.
•
Deduct.
Dif. of
HU.
Deduct.
1
.4305
31
17.6627
1
.0015
81
1.4830
2
.8708
32
18.3708
2
.00^
32
1.6802
3
1.3194
33
19.0972
3
.0139
83
1.6806
4
1.7777
34
19.8333
4
.0246
34
1.7839
5
2.2453
35
20.6787
5
.0885
36
1.8904
6
2.7222
36
21.3833
6
.0555
36
2.0000
7
3.2083
87
22.0972
7
.0766
37
2.1126
8
8.7037
88
22.8708
8
.0988
38
2.2284
9
4.2063
39
23.6627
9
.1250
39
2.3472
10
472SS2
40
244444
10
.1543
40
2.4691
11
5.2453
41
26.2453
11
.1867
41
2.6941
12
5.7777
42
26.0555
12
.2222
42
2.7222
13
6.3194
43
26.8760
13
.2608
43
2.8646
14
6.8708
44
27.7037
14
.3025
44
2.9876
15
7.4305
45
28.5146
15
.3472
45
3.1260
16
8.0000
46
29.3888
16
.8951
46
3.2654
17
8.6787
47
80.2463
17
.4460
47
8.4089
18
9.1666
48
"31.1111
18
.6000
48
a5665
19
9.7638
49
81.9861
19
.5671
49
3.7052
20
10.3703
50
82.8708
20
.6173
60
3.8680
21
10.9861
51
33.7638
21
.6805
61
40139
22
11.6111
52
34.6666
22
.7469
62
41728
23
12.2453
53
36.5787
23
.8163
63
4.33^
24
12.8888
54
86.6000
24
.8889
54
4.6000
25
13.5416
55
87.4305
26
.9647
56
46682
26
14.2037
56
38.3703
26
1.0432
56
48395
27
14.8760
67
89.8194
27
1.1250
67
5.0189
28
15.5655
68
40.2777
28
1.2099
58
6.1913
29
16.2453
69
41.2458
29
1.2978
59
5.3719
30
16.9444
1
60
42.2222
30
1.3889
60
6.5566
( xxxii. )
BASE 23— SLOPE i to 1.
1
Add.
1
•s
Add.
Deduct.
s a
Deduct.
1
a
Q
o
31
.4351
31
22.1018
1
.0031
2.9660
2
.8888
32
23.1111
2
.0123
32
3.1605
3
1.3611
33
24.1388
3
.0278
33
3.6111
4
1.8518
34
25.1851
4
.0494
34
3.5679
6
2.3610
35
2&2500
6
.0772
35
3.7808
1
6
2.8888
36
27.3333
6
.1111
36
4.0000
7
3.4351
37
28.4351
7
.1512
37
4.2263
8
4.0000
38
29.5555
8
.1976
38
4.4568
9
4.5833
39
30.6944
9
.2600
39
46944
10
5.1851
40
31.8618
10
.3086
40
49383
11
5.8055
41
33.0277
11
.3734
41
5.1883
12
&4444
42
342222
12
.4444
42
5.4444
13
7.1018
43
35.4351
13
.6216
43
5.7076
14
7.7777
44
36.6666
14
.6049
44
5.9753
15
8.4720
45
37.9166
15
.6944
46
6.2500
16
9.1851
46
39.1851
16
.7901
46
6.5308
17
a9166
47
40.4720
17
.8920
47
6.8179
18
10.6666
48
41.7777
18
1.0000
48
7.1111
19
11.4351
49
43.1018
19
1.1142
49
7.4104
20
12.2222
60
44.4444
20
1.2346
60
7.7160
21
13.0278
51
46.8055
21
1.3611
51
8.0277
22
13.8518
52
47.1851
22
1.4938
52
8.3456
23
14.6944
53
48.6833
23
1.6327
53
8.6697
24
15.5555
54
50.0000
24
1.7778
64
9.0000
25
16.4351
55
61.4351
26
1.9295
66
9.3364
26
17.3333
56
62.8888
26
2.0864
66
9.6790
27
18.2500
57
54.3611
27
2.2500
67 10.0277
28
19.1851
58
55.8518
28
2.4197
58 ;10.3827
29
20.1388
59
57.3611
29
2.5956 69 10.7438
30
21.1111
60
68.8688
30
2.7778 60 ill.llll
( xxxiiL )
BASE 23— SLOPE i to 1.
Add.
i
Add.
ssas
Deduct.
Dednct.
as
9B
O
a
1
.4397
31
26.6609
1
.0046
91
4.4490
2
.9073
32
27.8518
2
.0185
32
4.7407
Z
1.4028
33
29.1805
3
.0416
33
6.0416
4
1.9259
34
30.5369
4
.0740
34
6.3618
5
2.4767
36
31.9213
6
-1167
36
6.6712
6
3.0555
36
33.8333
6
.1667
36
6.0000
7
3.6619
37
34.7731
7
.2268
37
6.3379
8
4.2962
38
36.2407
8
.2963
38
6.6861
9
4.9583
39
37.7361
9
.3760
39
7.0416
10
5.6480
40
39.2592
10
.4630
40
7.4074
11
6.3657
41
40.8101
11
.5602
41
7.7824
12
7.1111
^
42.3888
12
.6667
42
8.1666
13
7.8842
43
43.9963
13
.7824
43
8.6612
14
8.6851
44
46.6296
14
.«)74
44
8.9^29
16
9.6137
46
47.2916
16
1.0417
46
9.3760
16
10.3704
46
48.9816
16
1.1862
46
9.7962
17
11.2646
47
60.6990
17
1.3379
47
10.2268
18
12.1666
48
32.4444
18
1,5000
48
10.6666
19
iai064
49
64.2176
19
1.6713
49
11.1167
20
14.0740
6§
66.0186
20
1.8518
60
11.6740
21
16.0695
61
57.8^2
21
2.0417
61
12.0416
22
16.0925
62
69.7037
22
2.2407
62
12.6186
23
17.1435
63
6L5880
23
2.4491
63
13.0046
24
18.2222
64
63.6000
24
2.6667
54
13.5000
25
19.3286
65
66.4397
25
2.8935
65
14.0046
26 20.4629
66
67.4074
26
3.1296
56
14.6186
27
21.6250
67
6a4028
27
3.3750
57
16.0416
28
22.8147
58
71.4289
28
3.6296
68
15.6740
29
24.0323
69
73.4767
29
3.8936
69
1&1157
30
26.2777
60
75.6666
30
4.1667
60 1&6666
F
( xxxiv. )
BASE 23— SLOPE 1 to 1.
1
Add.
}
31
Add.
Dif. of
Hts.
Deduct.
Dif. of
Ht8.
Deduct.
1
.4444
31.0000
1
.0062
31
5.9321
2
.9268
32
32.6926
2
.0247
32
6.3210
3
1.4444
33
34.2222
3
.0666
33
6.7222
4
2.0000
34
35.8888
4
.0988
34
7.1358
5
2.6926
35
37.6026
5
.1543
36
7.6617
6
3.2222
36
39.3333
6
.2222
36
8.0000
7
3.8888
37
41.1111
7
.3026
37
8.4506
8
4.5926
38
42.9260
8
.3951
38
8.9135
9
5.3333
39
44.7777
9
.5000
39
9.3888
10
6.1111
40
46.6666
10
.6173
40
9.8765
11
&9258
41
48.6926
11
.7469
41
10.3766
12
7.7777
42
50.6665
12
.8889
42
10.8888
13
8.6666
43
62.6555
13
1.0432
43
11.4136
14
9.6926
44
64.5926
14
1.2099
44
11.9506
15
10.6565
45
56.6666
15
1.3889
45
12.5000
16
11.6656
46
68.7777
16
1.5802
46
13.0617
17
12.5926
47
60.9260
17
1.7839
47
13.6358
18
13.6666
48
63.1111
18
2.0000
48
142222
19
14.7777
49
65.3333
19
2.2284
49
14.8209
20
16.9268
60
67.5926
20
2.4691
50
15.4321
21
17.1111
51
69.8888
21
2.7222
51
16.0555
22
18.3333
52
72.2222
22
2.9876
52
16.6913
23
19.5926
63
74.5926
23
3.2664
53
17.3395
24
20,8888
64
77.0000
24
3.5555
64
18.0000
26
22.2222
66
79.4444
25
3.8530
66
18.6728
26
23.5926
66
81.9258
26
4.1728
56
19.3680
27
25.0000
57
84.4444
27
4.6000
57
20.0565
28
26.4444
58
87.0000
28
4.8396
68
20.7654
29
27.9268
69
89.6926
29
6.1913
59
21.4876
30
29.4444 60 1
92.2222 30 1
5.5566 60
22.2222
1
( XXXV. )
BASE 23— SLOPE IJ to 1.
•8
Add.
1
Add.
if. of
Deduct.
if. of
[Its.
Deduct.
a
1
K
P
31
.4490
31
35.4490
1
.0077
7.4161
2
.9444
32
37.3333
2
.0309
32
7.9012
8
1.4861
33
39.2640
3
.0694
33
8.4027
4
2.0741
34
41.2406
4
.1234
34
8.9197
5
2.7081
36
43.2640
6
.1928
36
9.4621
6
3.8888
36
45.3333
6
.2778
36
10.0000
7
4.1156
37
47.4490
7
.3781
37
10.6632
8
4.8888
38
49.6111
8
.4938
38
11.1419
9
5.7083
39
51.8193
9
.6260
39
11.7361
10
6.5740
40
54.0740
10
.7716
40
12.3456
11
7.4862
41
66.3760
11
.9336
41
12.9706
12
8.4444
42
58.7222
12
1.1111
^
13.6111
13
9.4490
43
61.1157
13
1.3040
43
14.2680
14
10.6000
44
63.5566
14
1.6123
44
14.9382
Id
11.5971
46
66.0417
15
1.7361
46
16.6250
16
12.7407
46
68.5740
16
1.9753
46
16.3271
17
13.9303
47
71.1528
17
2.2299
47
17.0447
18
16.1666
48
73.7777
18
2.6000
48
17.7777
19
16.4490
49
76.4490
19
2.7865
49
18.5262
20
17.7777
60
79.1666
20
3.0864
50
19.2901
21
19.1528
51
81.9303
21
3.4028
51
20.0694
22
20.5740
62
84.7407
22
3.7346
62
20.8641
23
22.0417
53
87.5972
23
4.0818
53
21.6743
24
23.5556
64
90.5000
24
4.4444
64
22.5000
25
25.1167
55
93.4490
26
4.8228
65
23.3410
26
26.7222
66
96.4444
26
6.2160
66
24.1975
27
28.3750
57
99.4861
27
5.6250
57
26.0694
28
30.0740
68
102.5740
28
6.0494
58
25.9567
29
31.8193
69
106.7083
29
6.4891
69
26.8696
30
33.6111
60
108.8888
30
6.9444
60
27.7777
>
( xxxvi. )
BA8E 23— SLOPE IJ to 1.
1
•8
Add.
1
Add.
if. of
Deduct.
2-a
Deduct.
a
a
o
o
1
.4536
31
39.8982
1
.0092
31
8.8981
2
.962»
32
^0741
2
.0370
32
9.4815
3
1.5278
33
44.3055
3
.0833
33
10.0838
4
2.1481
34
4&6026
4
.1480
34
10.7037
5
2.8238
35
48.9352
6
.2313
36
11.3425
6
3.5555
36
51.3333
6
.3333
36
12.0000
7
4.3426
37
6a78e9
7
.4537
37
12.6759
8
6.1861
38
66.2964
8
.5926
38
13.370a
9
6.0833
39
68.8610
9
.7500
89
14.063»
10
7.0370
40
31.4814
10
.926»
40
148148
11
8.0464
41
641574
11
1.1203
41
16.6648
12
9.1111
42
66.8888
12
1.3333
42
16.3333
13
10.2314
431
69.6759
13
1.6648
43
17.1202
14
11.4074
44
72.6185
14
1.8148
44
17.9259
15
12.6387
45
76.4167
15
2.0833
45
18.7600
16
13.9259
46
78.3703
16
2.3704
46
19.6926
17
16.2682
47
81.3796
17
2.6769
47
20.4537
18
16.6666
48
84.4444
18
3.0000
48
21.3333
19
18.1203
^
87.6647
19
8.3426
49
22.2314
20
19.6296
50
90.7407
20
3.7037
60
2ai481
21
21.1945
61
93.9720
21
40833
61
24.0833
22
22.8148
52
97.2892
22
44816
52
25.0370
23
24.^68
63
100.6018
2a
48981
53
26.0092
24
26.2222
54
1040000
24
6.3333
64
27.0000
25
28.0092
55
107.4536
26
6.7860
66
28.0092
26
29.8618
50
110.9^29
26
6.2592
66
29.0370
27
31.7600
57
1145278
27
6.7500
57
80.0833
28
33.7087
58
118.1481
28
7.2692
68
31.1481
29
36.7128
69
121.8238
29
7.7869
59
32.2314
30
37.7777
60
126.6566
30
8.3333
60
33.3383
( xzxvii. )
BASE 23— SLOPE 1» to 1.
1
Xdi.
1
Add.
if. of
Deduct.
if. of
Deduct.
s
•
n
1
Q
1
.4581
31
443473
.0108
31
10.3811
2
.9815
32
46.8148
2
.0432
32
11.0609
3
1.5695
33
'^.3473
3
.0972
33
11.7638
4
2.2222
34
51.9444
4
.1728
34
12.4876
5
2.9395
35
546065
5
.2700
35
13.2330
&
3.7222
36
57.3333
6
.3889
36
14.0000
7
4.5696
37
60.1250
7
.5293
37
147885
8
5.4814
38
62.9815
8
.6913
38
15.6987
9
6.458a
39
65.9027
9
.8760
39
1&4305
10
7.6000
40
68.8888
10
1.0602
40
17.2839
11
8.6065
41
71.9399
11
1,3071
41
18.1589
12
9.7777
42
75.0555
12
1.5555
42
190565
13
11.0138
43
78,2362
13
1.8256
43
19.9747
14
12.3147
44
81.4814
14
2.1173
44
20.9135
15
ia6803
45
84.7916
15
2.4305
45
21.8750
16
15.1111
46
88.1666
16
2.7654
46
22.8680
17
16.6065
47
91.6065
17
3.1219
47
23.8626
18
18.1666
48
95.1111
18
3.5000
48
24.8888
19
19.7916
49
98.6803
19
3.8997
49
26.9367
20
21.4814
50
102.3147
20
43210
50
27.0061
21
23.2362
51
106.0138
21
47639
51
28.0972
22
25.0555
52
109.7777
22
6.2284
52
29.209&
23
26.9399
53
113.6065
23
5.7145
53
30.3441
24
28.8888
54
117.6000
24
6.2222
54
31.5000
25
30.9027
55
121.4583
25
6.7516
55
32.6774
26
32.9815
56
125.4814
26
7.3024
56
33.8765
27
35.1250
57
129.5696
27
7.8750
57
35.0972
28
37.3333
58
133.7222
28
8.4691
68
36.3394
29
39.6065
59
137.9395
29
9.0648
69
37.6033
30
41.9444
60
142.2222
30
9.7222
60
tJOaOOOO
( xxxviii. )
BASE 23— SLOPE 2 to 1.
•
M Hdght
Add.
•4^
•a
•s
Add.
tax
a
1
Deduct.
a
31
Dedact.
.4629
31
48.7962
.0123
11.8642
2
1.0000
32
51.5555
2
.0494
32
12.6419
3
1.6111
33
54.3888
3
.1111
33
13.4444
4
2.2962
34
57.2962
4
.1975
34
14.2716
5
3.0555
35
60.2777
5
.3086
35
16.1234
6
3.8888
36
63.3333
6
.4444
36
16.0000
7
4.7962
37
66.4629
7
.6049
37
16.9012
8
5.7777
38
69.6666
8
.7901
38
17.8271
9
6.8333
39
72.9444
9
1.0000
39
18.7777
10
7.9629
40
76.2962
10
1.2346
40
19.7530
11
9.1666
41
79.7222
11
1.4938
41
20.7530
12
10.4444
42
83.2222
12
1.7778
42
21.7777
13
11.7962
43
86.7962
13
2.0864
43
22.8271
14
13.2222
44
90.4444
14
2.4197
44
23.9012
15
14.7222
45
94.1666
15
2.7778
46
25.0000
16
16.2962
46
97.9689
16
3.1605
46
26.1234
17
17.9444
47
101.8333
17
3.5679
47
27.2716
18
19.6666
48
105.7777
18
4.0000
48
28.4444
19
21.4629
49
109.7962
19
4.4568
49-
29.6420
20
23.3333
50
113.8888
20
4.9382
50
30.86^
21
25.2777
51
118.0555
21
5.4444
51
32.1111
22
272962
52
122.2962
22
6.9753
52
33.3827
23
29.3888
53
126.6111
23
6.5309
63
34.6790
24
31.5555
54
131.0000
24
7.1111
54
36.0000
25
33.7962
55
135,4629
25
7.7160
65
37.3456
26
36.1111
56
140.0000
26
8.3457
56
38.7160
27
38.5000
67
144.6111
27
9.0000
57
40.1111
28
40.9629
58
149.2962
28
9.6790
58
41.5308
29
43.5000
59
154.0555
29
10.3827
59
42.9753
30
46.1111
60
158.8888 1 30
11.1111
60
44.4444
( xzxix. )
BASE 23— SLOPE 2J to 1.
•s
Add.
S
Add.
5a BB
Deduct.
Deduct.
a
X
Q
Q
1
.4722
31
67.6946
1
.0154
31
148302
2
1.0370
32
61.0370
2
.0617
32
16.8013
3
1.6946
33
644722
3
.1389
33
16.8055
4
2.4444
34
68.0000
4
.2468
34
17.8396
5
3.2870
36
71.6203
6
.3857
35
18.9043
6
42222
36
75.3333
6
.5566
36
20.0000
7
6.2500
37
79.1387
7
.7661
37
21.1266
8
6.3703
38
83.0370
8
.9876
38
22.2839
9
7.6833
39
87.0276
9
1.2600
39
23.4722
10
8.8888
40
91.1111
10
1.6432
40
24.6913
11
10.2870
41
96.2870
11
1.8673
41
25.9413
12
11.7777
42
99.5655
12
2.2222
42
27.2222
13
13.3611
43
103.9166
13
2.6080
43
28.5360
14
16.0370
44
108.3703
14
3.0247
44
29.8765
16
16.8056
46
112.9166
16
3.4722
45
31.2600
16
18.6666
46
117.6665
16
3.9606
46
32.6643
17
20.6203
47
122.2870
17
44599
47
34.0895
18
22.6666
48
127.1111
18
5.0000
48
35.5556
19
24.8056
49
132.0277
19
5.5710
49
37.0524
20
27.0370
60
137.0370
20
6.1728
50
38.5802
21
29.3611
61
142.1388
21
6.8055
61
40.1388
22
31.7777
52
147.3333
22
7.4691
62
41.7283
23
34.2870
63
152.6203
23
8.1636
63
43.3487
24
36.8888
64
158.0000
24
8.8889
54
45.0000
26
39.5833
65
163.4722
25
9.6466
66
46.6820
26
42.3703
66
169.0370
26
10.4321
56
48.3950
27
46.2600
57
1746946
27
11.2600
67
60.1388
28
48.2222
58
180.4444
28
12.0587
58
51.9136
29
61.2870
69
186.2870
29
12.9782
69
63.7191
30
644444
60
192.2222
30
13.8889
60
66.6556
(xl.)
BASE 23— SLOPE 3 to 1.
1
Add.
1
Add.
Dedact.
2^
Deduct.
X
X
1
«
1
.4814
31
66.5926
.0185
31
17.7963
2
1.0740
32
70.5185
2
.0740
32
18.9630
3
1,7777
33
745555
3
.1667
33
20.1666
4
2.5926
34
78.7037
4
.2961
34
21.4074
5
3.5185
35
82.9629
5
.4628
35
22.6861
6
45555
36
87.3333
6
.6667
36
24.0000
7
5.7037
37
91.8147
7
.9074
37
25.3518
8
&g629
38
96.4074
8
1.1852
38
26.7407
9
8.3333
39
101.1111
9
1.6000
39
28.1666
10
9.8147
40
105.9259
10
1.8518
40
29.6296
11
11.4074
41
110.8518
11
2.2407
41
31.1296
12
13.1111
42
115.8888
12
2.6667
42
32.6666
13
149-259
43
121.0370
13
3.1296
43
34.2405
14
16.8518
44
126.2962
14
3.6296
44
36.8518
15
18.8888
45
131.6666
15
41667
46
37.5000
16
21.0370
46
137.1481
16
47407
46
39.1851
17
23.2962
47
142.7407
17
5.3518
47
40.9074
18
25.6666
48
148.4444
18
6.0000
48
42.6666
19
28.1481
^
154.2592
19
a6852
49
44.4629
20
30.7407
50
160.1852
20
7.4074
50
46.2963
21
33.4444
51
16a2222
21
8.1667
61
49.1666
fl2
3&2592
52
172.3703
22
8.9629
62
50.0740
23
39.1852
53
178.6296
23
9.79^
63
52.0185
24
42.2022
54
185.0000
24
10.6667
54
54.0000
25
45.3703
55
191.4814
25
11.6741
55
56.0184
26
48.6296
56
198.0740
26
12.5184
56
68.0640
27
52.0000
57
204.7777
27
13.5000
57
60.1666
28
55.4814
58
211.5926
28
145185
58
62.2962
29
69.0740
69
218.6186
29
16.6739
69
64.4629
30
62.7777
60
225.5555
SO
16.6667
60
66.6666
(xli.)
BASE 24— SLOPE i to 1.
-a,
•s
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Add.
.4490
.9074
1.3750
1.8518
2.3379
2.8333
3.3379
3.8518
4.3750
4.9074
5.4490
6.0000
6.5601
7.1-296
7.7083
8.2962
8.8935
9.5000
10.1157
10.7407
11.3750
12 0185
12.6712
13.3333
14.0046
14.6851
15.3750
16.0740
16.7824
17.5000
Add.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
18.2268
18.9629
19.7083
20.4629
21.2268
22.0000
22.7824
23.5740
24.3750
25.1851
26.0046
26.8333
27.6712
28.5185
29.3750
30.2407
31.1157
32.0000
32.8935
33.7962
347083
35.6296
36.5601
37.5000
38.4490
39.4074
40.3750
41.3518
42.3379
43.3333
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Deduct.
.0015
.0062
.0139
.0246
.0385
.0555
.0756
.0988
.1250
.1543
.1867
.2222
.2608
.3025
.3472
.3951
.4460
.5000
.5571
.6173
.6805
.7469
.8163
.8889
.9647
1.0432
1.1250
1.2099
1.2978
1.3889
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
a
Deduct.
1.4830
1.5802
1.6805
1.7839
1.8904
2.0000
2.1126
2.2284
2.3472
2.4691
2.5941
2.7222
2.8545
2.9876
3.1250
3.2654
3.4089
3.5555
3.7052
3.8580
4.0139
4.1728
4.3349
4.5000
4.6682
4.8395
5.0139
5.1913
5.3719
5.5555
I
\
( xlii. )
BASE 24^8LOPE J to 1.
•s
Add.
•s
Add.
S3 35
Deduct.
Deduct.
n
1
-
s
o"
31
. .4536
31
22.6759
1
.0031
2.9660
-.2
.9259
32
23.7037
2
.0123
32
3.1605
3.
.1.4167 33
.1.9269 34
24.7600
3
.0278
33
36111
4.
25.8147
4
.0494
34
3.5679
5
2.4636
35
26.8981
5
.0772
36
3.7808
6
3.0000
36
28.0000
6
,1111
36
4.0000
7
3.5647
37
29.1203
7
.1512
37
4.2253
8
4.1481
38
30.2692
8
.1975
38 4.4668
9
4.7600
39 31.4166
9
.2600
39
4.6944
10
6.3703
40 32.6926
10
.3086
40
4.9383
11
6.0092
41
33.7870
11 .3734
41
5.1883
12
6.6666
^
36.0000
12
AAAA
• X X J. X
^
5.4444
13
7.3^25
43
36.2314
13
.5216
43
6.7067
14
8.0370
44
37.4814
14
.6049
44
5.9763
16
8.7500
45
38.7600
15
.6944
46
6.2500
16
9.4814
46
40.0370
16
.7901
46
6.5308
17
10.2314
47
41.3426
17
.8920
47
6.8179
18
11.0000
48
'^.6666
18
1.0000
48
7.1111
19
11.7870'
49
44.0092
19
1.1142
49
7.4104
20
12.6926
60
46.3703
20
1.2346
60
7.7160
21
13.4167
61
46.7500
21
1.3611
51
8.0277
22
14.2592
62
48.1481
22
1.4938
62
8.3466
23
16.1203
53
49.5647
23
1.6327
63
8.6697
24
16.0000
54
51.0000
24
1.7778
64
9.0000
25
1&8981
66
62.4536
25
1.9295
55
9.3364
26
17.8147
56
63.9269
26
2.0864
56
9.6790
27
18.7500
57
66.4167
27
2.2500
67
10.0277
28
19.7037
58
66.9269
28
2.4197
58
1038-i7
29
20.6759
69
58.4536
29
2.5956
5;)
10.7438
30
21.6666
60
60.0000
30
2.7778
60
11.1111
( xliii. )
BASE- 24— SLOPE f to 1.
■a
•s
Add.
•t
Add.
Deduct.'
Deduct.
1
- • •TtvO^,
31
27.1250
1
.0046
31
4.4490
2
.•••ty^^TC
32
28.4444 .
2
.0185
32
'4.7407
3
a*:458,4;
33
29.7916
^ o«
<.041«;
33
6.^16
4
2:0600.
34
31.1666
•■'4
.0740.
^
5.3618
5
2.5692;
35
1
; 32.5692
1/ 6
11157
35
66712
6
3.1666
36.
S* 34.0000
6
.1667^
36
6.0000
7
3.7915
37.'
/.-35.4582
"7
.2268"
37
6.3379
8
4.4444
38
n 36.9444
8
.296S
38
6.6851
9
5.1250
39
• 38.4583
9
.3750
39
7.0416
10
5.8333
40
40.0000
10
.4630
40
7.4074
11
6.5694
41
41.5692
11
.5602
41
7.7824
12
7.3333
42
43.1666
12.
.6667
42
8.1666
13
8.1250
43
44.7916
13
-.7824
43
'8:6612
14
8.9444
44
46.4444
14.
.9074
44
8.9629
15.
9.7915
45
48.1250
16
1.0417
45
9.3750
tec
KB6666
46
49.8333
16
1.1852
46
'9:7962
17jt
iai56g2
47
51.5692
17.
1».3379
47
10V2268
I8&
1-2^5000
48
53.3333
18.
115000
48
10.6666
m
13.4584
49
55.1250
19
1.6713
49
11.1157
20.
14.4444
60
56.9444
20
1.8518
50
11.5740
21
15.4584
51
: 58.7916
21
20417
51
12.0416
22t
16.5000,
52
.60.6666
22
2.2407
62
12.6186
• ^O V
t:?:5692
•63i
;.62.5692
23
2.4491
63
13.0046
24,
*8)666a
,54
•64.5000
24
2.6667
64
13.5000
25.1
19.7916.
55
' 66.'4584
25
2.8935
56
14.0046
26-
20:9444
56-
68.4444
26
3.1296
56
14.5185
27,
22il250
67
70.4584
27
3.3750
57
15.0416
28
23.3333
68
72.5000
28
3.6296
58
15.6740
29
24.5692
59
74.5693
29
3.8935
59
16.1157
30
25.8333
60
76.6666
30
4.1667
60
16.6666
( ^liv. )
BASE 24— SLOPE 1 to 1.
1
Add.
4J
Add.
if. of
its.
Deduct.
Dedaot.
iS
n
Q"
Q
1
,4628
31
31.5741
I
.0062
31
5.9321
2
,9629
32
33.1851
2
.0247
32
6.3210
3
1.6000
33
34.3333
3
.0565
33
6.7222
4
2.0740
34
36.5185
4
.0988
34
7.1368
5
2.6850
35
38.2407
5
.1543
35
7.6617
6
3.3333
36
40.0000
6
.2222
36
8.0000
7
4.0185
37
41.7961
7
.3026
37
8.4606
8
4.7407
38
43.6296
8
.395 L
38
8.9135
9
5.5000
39
45.5000
9
.6000
39
9.3888
10
6.2962
40
47.4074
10
.6173
40
9.8765
11
7.1296
41
49.3518
11
.7469
41
10.3765
12
8.0000
42
51.3333
12
.8889
42
10.8888
13
8.9074
43.
63.3518
13
1.0432
43
11.4136
14
9.8518
44
65.4073
14
1.2099
44
11.9506
15
10.8333
45
57.6000
15
1.3889
45
12.6000
16
11.8518
46
59.6296
16
1.5802
46
13.0617
17
12.9074
47
61.7962
17
1.7839
47
13.6368
18
14.0000
48
64.0000
18
2.0000
48
14.2222
19
16.1296
49
66.2407
19
2.2284
49
14.8209
2D
16.2962
50
68.5185
20
2.4691
50
15.4321
21
17.5000
51
70.3333
21
2.7222
51
16.0655
22
18.7407
52
73.1851
22
2.9876
52
16.6913
23
20.0185
63
75.6741
23
3.2664
53
17.3395
24
21.3333
54
78.0000
24
3.5556
64
18.0009
25
22.6860
55
80.4628
26
3.8630
56
18.6728
26
24.0740
56
82.9629
26
4.1728
56
19.3680
27
26.5000
67
86.6000
27
4.6000
57
20.0565
28
26.9629
68
88.0741
28
4.8395
68
20.7654
29
28.4629
69
90.6860
29
5.1913
59
21.4876
30
30.0000
60
93.3333
30
5.5665
60
22.2322
( »lv. )
BASE 24— SLOPE 1^ to 1,
t
Add.
4^
1
Add.
|"S .
Deduct. I:«3m
Deduct.
X
X
q"
O"
1
.4674
31
36.0232
1
jomi
31
7.4151
2
.9814
32
37.9269
2
.0309
32
7.9012
8
1.6418
33
89.8760
3
.0694
33
8.4027
4
2.1482
34
41.8703
4
.1284
34
8.9197
5
2.8007
36
43.9120
6
.1928
36
9.4521
6
3.6000
36
46.0000
6
.2778
36
10.0000
7
4.2463
37
48.1340
7
.8781
37
10.5632
8
6.0370
38
60.3148
8
.4938
38
11.1419
9
5.8750
39
62.6416
9
.6250
39
11.7361
10
&7692
40
64.8148
10
.7716
40
12.3456
11
7.6898
41
67.1342
11
.9336
41
12.9706
12
8.6666
42
69.5000
12
1.1111
42
13.6111
13
9.6898
43
61.9120
13
1.8040
48
14.2680
14
10.7592
44
64.3703
14
1.5123
44
14.9382
15
11.8760
46
66.8750
16
1.7361
46
15.6250
16
13.0370
46
69.4259
16
1.9763
46
16.3271
17
14.2463
47
72.0231
17
2.2299
47
17.0447
18
16.5000
48
74.6666
18
2.5000
48
17.7777
19
16.8007
49
77.3564
19
2.7856
49
18.5262
20
18.1481
50
80J0926
20
3.0864
60
19.2901
21
19.6418
51
82.8750
21
3.4028
51
20.0694
22
20.9814
52
85.7086
22
3.7846
52
20.8641
23
22.4674
53
88.5785
23
4.0818
63
21.6743
24
24.0000
54
91.6000
24
4.4444
54
22.5000
26
26.6786
66
94.4674
26
4.8228
55
23.3410
26
27.2036
56
97.4814
26
6.2160
56
24.1975
27
28.8750
67
100.6418
27
6.^50
57
25.1694
28
30.5925
68
103.6481
28
6.0494
68
25.9567
29
32.3564
69
106.8007
29
6.4891
69
26.8595
30
34.1666
60
110.0000
30
6.9444
60
27,7777
( xlvi. )
BASE 24— SLOPE IJ to 1.
•a
Add.
4^
■a
•c
Add.
O J
Deduct.
Deduct.
93
1
s
1
31
.4720
31
40.4722
.0092
8.8981
2
1.0000
32
42.6666
2
.0370.
32
9,4815
3
1.5833
33
44.9166
3
.0833
33
10.0833
4
2.2222
34
47.2222
4
.1480
34
10.7037
5
2.9162
36
49.6833
5
.2313
36
11.3426
6
3.6666
36
52.0000
6
.3333
36
12:0000
7
4.4722
37
64.4719
7
.4637
37.
12.'6759
8
5.3333
38
67.0000
8
.5926
38.
13.3703
9
6.2500
39
59.5833
9
.7500
39.
14.0833
H)
7.2222
40
62.2222
10
.9259
40,
14.8148
11
8.2500
41
64.9166
11
1.1203
41.
15.5648
! 12
9.3333
42
67.6666
12
1.3333
42
16.3333
13
10.4722
43
70.4722
13
1.5648.
43
17.1202
14
11.6666
44
73.3333
14
1.8148
44
17.9269
16
12.9162
45
76.2600
15
2.0833.
46
18.7600
16
14.2222
46
79.2222
16
2.3704-
46
19.5925
17
16.5833
47
82.2600
17.
2:6759.
47
20.4637;
18
17.0000
48
86.3333
18
3.0000.
48..
21:3333.
19
18.4720
49
88.4720
19
3.3426
49;
22:2314
20
20.0000
50
92.6666
.20
3.7037
60
23.1481 .
21
21.5833
51
94.9166
21
4.0833.
61
24,0833
22
23.2222
62
98.2222
22
4.4816
62..
2^.P370
23
24.9166
53
101.5833
23
4.8981
63.
26:0092
24
26.6666
54
106.0000
24
6:3333
64
27.0000
25
28.4720
66
108.4720
25
5:7869
55
28.0092
26
30.3333
66
112.0000
26
6:2592
66
29.0370
27
32.2500
67
115.5833
27
6.7500.
57
30.0833
28
34.2222 58
119.2222
28
7.2592
58
31.1481
29
36.2500 69
122.9162
29
7.7869,
69
32.2314
1
30
38.3333 60
126.6666
30
8.3333
60
33.3333
1
( xlvii. )
BASE 24— SLOPE Ij to 1.
Height
• Add.
t
•s
31
Add.
Dif. of
Deduct.
(4-1
31
Deduct.
1
.4768
44.9214
1
.0108
10.3811
2
1.0185
32
47.4073
2
.0432
32
11.0609
3
1.6250
33
49.9583
3
.0972
33
1 1.7638
4
2.2963
34
62.5740
4
.1728
34
12.4876
5
3.0319
35
56.2646
6
.2700
35
13.2330
6
3.8333
36
68.0000
6
.3889
36
14.0000
7
4.6990
37
60.8102
7
.6293
37
14.7885
8
5.6296
38
63.6862
8
.6913
38
15.5987
9
6.6250
39
66.6250
9
.8760
39
16.4305
10
7.6851
40
69.6296
10
1.0802
40
17.2839
11
8.8102
41
72,6990
11
1.3071
41
18.1589
12,
10.0000
42
76.8333
12
1.5555
42
19.0555
13
11.2546
43
79.0319
13
1.8266
43
19.9747
14
12:5740
44
82.2962
14
2.1173
44
20.9135
15
13.9583
45
85.6-250
15
2.4306
45
21.8750
16
15.4074
46
89.0186
16
2.7654
46
22.8580
17
16,y214
47
92.4768
17
3.1219
47
23.8626
18
18.5000
48
96.0000
18
3.6000
48
24.8888
19
20.1435
49
99.6878
19
3.8997
49
25.9367
20
21.8518
50
104.2407
,20
4.3210
50
27.0061
21
23.6250
51-
106.9683
21
4.7639
51
28.0972
22
25.4629
62
110.7407
22
6.2284
52
29.2098
ii3
27.3658
53
114.6878
23
6.7145
53
30.3441
24
29.3333
54
118.51)00
24
6.2222
54
31.5000
25
31.3658
65.
122.4768
25
6.7516
55
32.6774
26
33.4629
56
126.5186
26
7.3024
56
33.8765
27
35.6250
67
l:i0.6'.i50
27
7.8750
57
35.0972
28
37.8518
58
134.7962
28
8.4691
58
36.^394
29
40.1435
69
139.0319
29 ,9.0848
59
37.6033
30
42.5000
60
143.3333
30 1
9.7222 1
60
38.8888
( xlviii. )
BASE 24-.SLOPE 2 to 1.
•4^
Add.
SB
31
Add.
gSB
1
Deduct.
<»4
31
Deduct.
1
.4814
49.3704
.0123
11.8642
2
1.0370
32
52.1480
2
.0494
32
12.6419
8
1.6666
33
65.0(100
3
.1111
33
13.4444
4
2.3704
34
57.9257
4
.1975
34
14.2716
6
3.1480
35
60.9257
5
.3086
35
15.1234
6
4.0000
36
64.0000
6
.4444
36
16.0000
7
4.9257
37
67.1480
7
.6049
37
16.9012
8
5.9257
38
70.3704
8
.7901
38
17.8271
9
7.00(J0
39
73.6666
9
1.0000
39
18.7777
10
8.1480
40
77.0370
10
1.2346
40
19.7630
11
9.3704
41
80.4814
11
1.4938
41
20.7530
12
10.6666
42
84.0000
12
1.7778
42
21.7777
13
12.0370
43
87.5926
13
2.0864
43
22.8271
14
13.4814
44
91.2690
14
2.4197
44
23.9012
15
15.0000
45
95.0000
15
2.7778
45
25.0000
16
16.5926
46
98.8149
16
3.1605
46
26.1234
17
18.2590
47
102.7036
17
3.5679
47
27.2716
18 J20.0000
48
106.6666
18
4.(X)00
48
28.4444
19 21.8150
49
110.7036
19
4.4568
49
29.6420
20 23.7036
50
115.8149
20
4.9382
50
30.8642
21
25.6666
51
119.0000
21
5.4444
51
32.1111
22
27.7036 ! 52
123.2890
22
5.9753
52
33.3827
23 129.8149:53
127.5926
23
6.5309
53 34.6790
24 j32.0000|54
132.0000
24
7.1111
64 36.0000
25 34.-2590J 55
136.4814
25
7.7160
56 37.3456
26 36.5926
56
141.0370
26
8.3457
66 38.7160
27 '39.0000:57
145.0H66
27
9.0000
57
40.1111
28
41.4814(58
150.3704
28
9.6790
68
41.5308
29
44.0370 : 59
165.1480
29
10.3827
59
42.9753
30
46.6666
160
160.0000]
30
11.1111
60
44.4444
( xlix. )
BASE 24— SLOPE 2J to 1.
•s
Add.
1
s
Add.
Dif.of
Hts.
D«dact.
Dif.of
Hts.
Deduct.
1
.4906
31
68.2686
1
.0164
31
148302
2
1.0740
32
61.6296
2
.0617
32
15.8016
3
1.7600
33
66.0834
3
.1389
33
16.8065
4
2.5185
34
68.^96
4
.2468
34
17.8395
5
3.3796
35
72.2686
5
.3867
35
18.9043
6
43333
36
76.0000
6
.5555
36 20.0000 1
7
6.3796
37
79.8240
7
.7661
37
21.1266
8
6.6185
38
83.7407
8
.9876
38
22.2839
9
7.7600
39
87.7600
9
1.2500
39
23.4722
10
9.0740
40
91.8518
10
1.6432
40
246913
11
10.4900
41
96.0460
11
1.8673
41
25.9413
12
12.0000
^
100.3333
12
2.2222
42
27.2222
13
13.6018
43
104.7131
13
2.6080
48
28.5360
14
15.2962
44
109.1851
14
3.0247
44
29.8765
15
17.0833
46
113,7500
16
3.4722
45
31.2500
16
18.9629
46
118.4074
16
8.9506
46
32.6543
17
20.93^
47
123.1576
17
44699
47
340896
18
23.0000
48
128.0000
18
6.0000
48
35.5565
19
26.1576
49
132.9349
19
5.6710
49
37.0624
20
27.4074
50
138.9629
20
6.1728
50
38.5802
51
2a7600
51
14a0633
21
6.8066
51
40.1388
22
32.1851
52
148.2962
22
7.4691
52
41.7288
58
34.7131
53
153.6018
23
8.1636
53
43.3487
24
37.3333
64.
169.0000
24
8.8889
54
45.0000
25
40.0460
55
164.4906
26
9.6455
65
46.6820
26
42.8618
56
170.0740
26
ia4321
56
48.3950
27
46.7500
57
176.7500
27
11.2500
67
60.1388
28
48.7407
58
181.5186
28
12.0587
68
61.9185
29
61.8240
59
187.3796
29
12.9782
69
58.7191
•30
55.0000
60
193.3333
30
13.8889
60
H
55.6666
BASE 24— SLOPE 3 to 1.
Add.
1
Add.
if. of
Hts.
Deduct.
if. of
Hts.
Deduct.
s
X
O
Q
•
1
.6000
31
67.1666
1
.0185
31
17.7963
2
1.1111
32
71.1111
2
.0740
32
18.9630
3
1.8333
33
76.1666
3
.1667
33
20.1666
4
2.6666
34
79.3333
4
.2961
34
21.4074
5
3.6111
35
83.6111
6
.4628
36
22.6851
6
4.6666
36
88.0000
6
.6667
36
24.0000
7
5.8333
37
92.5000
7
.9074
37
26.3618
8
7.1111
38
97.1111
8
1.1862
38
26.7407
9
8.6000
39
101.8333
9
1.5000
39
28.1666
10
10.0000
40
106.6666
10
1.8618
40
29.6296
11
11.6111
41
111.6111
11
2.2407
41
31.1296
12
13.3333
42
116.6666
12
2.6667
42
32.6666
13
15.1666
43
121.8333
13
3.1296
43
34.2405
14
17.1111
44
127.1111
14
3.6296
44
35.8518
15
19.1666
45
132.5000
16
4.1667
45
37.5000
16
21.3333
46
138.0000
16
4.7407
46
39.1851
17
23.6111
47
143.6111
17
6.3618
47
40.9074
18
26.0000
48
149.3333
18
6.0000
48
42.6666
19
28.6000
49
155.1666
19
6.6862
49
44.4629
20
31.1111
60
162.1111
20
7.4074
50
46.2963
21
33.8333
51
167.1666
21
8.1667
51
49.1666
22
36.6666
52
173.3333
22
8.9^9
62
50.0740
23
39.6111
53
179.6111
23
9.7962
53
52.0186
24
42.6666
54
186.0000
24
10.6667
54
64.0000
25
45.8333
55
192.6000
26
11.5741
65
66.0184
26
49.1111
56
199.1111
26
12.5184
56
68.0640
27
52.5000
57
206.8333
27
13.6000
57
60.1666
28
56.0000
58
212.6666
28
14.6185
58
62.2962
29
^.6111
59
219.6111
29
16.5739
59
64.4629
30
63.3333
60
226.6666
30
16.6667
60
66.6666
J
( li- )
BASE 25-SLOPE i to 1.
-a
*
I
".a
"Sa
•8
Add.
•s
Add.
SaSJ
Deduct.
■sn
Deduct.
X
X
a
o
1
.4676
31
18.8009
1
.0015
31
1.4830
2
.9444
32
19.6555
2
.0062
32
1.6802
3
1.4305
33
20.3194
3
.0139
33
1.6805
4
1.9259
34
21.0925
4
.0246
34
1.7839
5
2.4305
35
21.8760
6
.0385
35
1.8904
6
2.9444
36
22.6666
6
.0555
36
2.0000
7
3.4676
37
23.4676
7
.0766
37
2.1126
8
4.0000
38
24.2777
8
.0988
38
2.2284
9
4.5416
39
25.0972
9
.1250
39
2.3472
10
5.0926
40
25.9259
10
.1543
40
2.4691
11
5.6528
41
26.7639
11
.1867
41
2.5941
12
6.2222
42
27.6111
12
.2222
42
2.7222
13
6.8009
43
28.4676
13
.2608
43
2.8545
14
7.3888
44
29.3333
14
.3025
44
2.9876
15
7.9861
45
30.2083
15
.3472
45
3.1250
16
8.5925
46
31.0925
16
.3951
46
3.2654
17
9.2083
47
31.9861
17
.4460
47
3.4089
18
9.8333
48
32.8888
18
.6000
48
3.5666
19
10.4675
49
33.8009
19
.5671
49
3.7052
20
11.1111
50
34.7222
20
.6173
50
3.8680
21
11.7639
51
35.6528
21
.6806
51
4.0139
22
12.4259
52
36.5926
22
.7469
52
4.1728
23
13.0972
53
37.5416
23
.8163
53
4.3349
24
13.7777
54
38.5000
24
.8889
54
45000
25
14.4676
55
39.4676
25
.9647
56.
4.6682
26
15.1666
56
40.4444
26
1.0432
56
4.8395
27
15.8760
57
41.4305
27
1.1250
67
6.0139
28
16.5925
58
42.4259
28
1.2099
58
5.1913
29
17.3194
59
4.3.4305
29
1.2978
59
6.3719
30 18.0555
•
60
44.4444
30
1.3889
60 6.6555
( lii- )
BASE 26— SLOPE i to 1.
1
Add.
•r
w
Add.
1
Deduct.
2«
31
Deduct.
1
.4722
31
23.2600
.0031
2.9660
2
.9629
32
242962
2
.0123
82
3.1605
3
1.4722
33
25.3611
3
.0278
33
3.6111
4
2.0000
34
26.U4A
4
.0494
34
3.6679
5
2.6462
36
27.5463
5
.0772
36
3.7808
6
3.1111
36
28.6666
6
.1111
36
4.0000
7
3.6944
37
29.8056
7
.1612
37
4.2253
8
4.2963
38
30.9629
8
.1976
«JO
4.4568
9
4.916&
39
32.1388
9
.2500
39
4.6944
10
5.6665
40
33.3333
10
.3086
40
4.9383
11
6.2130
41
34.6463
11
.3734
41
5.1883
12
6.8888
42
36.7777
12
.4444
42
5.4444
13
7.5833
43
37.0277
13
.6216
43
5.7076
14
8.2962
44
38.2962
14
.6049
44
6.9763
15
9.0277
46
39.6833
16
.6944
46
6.2500
16
9.7777
46
40.8888
16
.7901
46
6.5306
17
10.5462
47
42.2129
17
.8920
47
6.8179
18
11.3333
48
43.6556
18
1.0000
48
7.1111
19
12.1388
49
44.9166
19
1.1142
43
7.4104
20
12.9629
60
4&2963
20
1.2346
60
7.7160'
21
13.8055
51
47.6944
21
1.3611
51
8.0277
22
14.6666
62
^.1111
22
1.4938
m
8.3456
23
15.5462
53
50.6462
23
1.6327
53
8.669T
24
16.4444
54
52.0000
24
1.7778
64
9.0000
25
17.3611
56
53.4722
26
1.9296
55
9.3364
26
18.2962
56
54.9629
26
2.0864
56
9.6790
27
19.2500
57
56.4722
27
2.2600
57
10.0277
28
20.2222
58
58.0000
28
2.4197
68
10.3827
29
21.2129
69
69.6462
29
2.5956
59
10.7438
30
22.2222
60
61.1111
30
2.7778
60
11.1111
(liii
•)
BASE 26 SLOPE f to 1.
X
1
Add.
t
Add.
Dif.of
Hts.
Deduct.
Dif. of
Hts.
DedDct.
.4768
31
27.6991
1
.0046
31
4.4490
2
.9815
32
29.0370
2
.0185
32
4.7407
3
1.6139
33
30.4028
3
.0416
33
6.0416
4
2.0741
34
31.7962
4
.0740
34
5.3618
6
2.6619
36
33.2176
6
.1157
36
6.6712
6
3.2777
36
346666
6
.1667
36
6.0000
7
3.9212
37
36.1434
7
.2268
37
6.3379
8
4.5926
38
37.6481
8
.2963
38
6.6851
9
5.2916
39
39.1806
9
.3760
39
7.0416
10
6.0184
40
40.7407
10
.4630
40
7.4074
11
6.7732
41
42.3288
11
.6602
41
7.7824
12
7.6555
42
43.9444
12
.6667
42
8.1666
13
8.3667
43
45.5879
13
.7824
43
8.6612
14
9.2036
44
47.2592
14
.9074
44
8.9629
15
10.0603
45
48.9583
15
1.0417
46
9.3760
16
10.9620
46
50.6851
16
1.1862
46
9.7962
17
11.8842
47
52.4397
17
1.3379
47
10.2268
18
12.8333
48
64.2222
18
1.6000
48
10.6666
19
13.8101
49
66.0323
19
1.6713
49
11.1167
20
14.8147
60
67.8704
20
1.8518
60
11.6740
21
15.8472
51
^.7361
21
2.0417
61
12.0416
22
16.9074
52
61,6296
22
2.2407
52
12.6185
23
17.9953
63
63.6608
23
2.4491
63
13.0046
24
19.1111
54
66.5000
24
2.6667
54
13.6000
26 20.2646
66
67.4768
26
2.8935
65
14.0046
26 21.4258
66
69.4814
26
3.1296
56
14.5185
27 122.6250
67
71.6139
27
3.3760
57
15.0416
28 23.8518
68
73.6741
28
3.6296
58
15.5740
29 :25.1064
69
76.6619
29
3.8935
69
16.1167
30 126.3888
60
77.7777
30
4.1667
60
16.6666
(liv
.)
BASE 26— SLOPE 1 to 1.
}
Add.
•a,
•s
Add.
(M
Z^
SW
Deduct.
Deduct.
33
a
a
1
Q
1
.4814
31
32.1481
.0062
31
6.9321
2
1.0000
32
33.7777
2
.0247
32
6.3210
3
1.5655
33
35.4444
3
.0655
33
6.7222
4
2.1481
34
37.1481
4
.0988
34
7.1358
5
2.7777
36
38.8888
5
.1543
36
7.5617
6
3.4444
36
40.6666
6
.2222
36
8.0000
7
4.1481
37
42.4814
7
.3026
37
8.4506
8
4.8888
38
44.3333
8
.3951
38
8.9136
9
6.6666
39
46.2222
9
.5000
39
9.3888
10
6.4814
40
48.1481
10
.6173
40
9.8766
11
7.3333
41
60.1111
11
.74^
41
10.3766
12
8.2222
42
62.1111
12
.8889
42
10.8888
13
9.1481
43
64.1481
13
1.0432
43
11.4136
14
10.1111
44
56.2222
14
1.2099
44
11.9506
15
11.1111
45
68.3333
16
1.3889
46
12.5000
16
12.1481
46
60.4814
16
1.5802
46
13.0617
17
13.2222
47
62.6666
17
1.7839
47
13.6368
18
14.3333
48
64.8888
18
2.0000
48
14.2222
19
16.4814
49
67.1481
19
2.2284
49
14.8209
20
16.6666
60
69.4444
20
2.4691
60
16.4321
21
17.8888
61
71.7777
21
2.7222
61
16.0655
22
19.1481
52
74.1481
22
2.9876
62
16.6913
23
20.4444
53
76.6666
23
3.2654
63
17.3395
24
21.7777
54
79.0000
24
3.5556
64
18.0000
25
23.1481
55
81.4814
26
3.8530
56
18.6728
26
24,5555
66
84.0000
26
4.1728
66
19.3580
27
26.0000
57
86.5655
27
4.5000
67
20.0556
28
27.4814
68
89.1481
28
4.8395
58
20.7654
29
29.0000
59
91.7777
29
6.1913
69
21.4876
30
30.5555
60
94.4444
30
6.5555
60
22.2222
(Iv.
)
BASt; 25— SLOPE 1^ to 1.
■
i
Add.
1
Add.
S3 33
Deduct.
Dednct.
1
B
O
31
.4860
3i
36.6973
1
.0077
7.4151
2
1.0185
32
38.6185
2
.0309
32
7.9012
3
1.6972
33
40.4861
3
.0694
33
8.4027
4
2.2222
34
42.5000
4
.1234
34
8.9197
5
2.8934
35
44.6601
5
.1928
35
9.4521
6
3.6111
36
46.6666
6
.2778
36
10.0000
7
4.3750
37
48.8192
7
.3781
37
10.5632
8
5.1861
38
51.0185
8
.4938
38
11.1419
9
6.0416
39
53.2368
9
.6250
39
11.7361
10
6.9444
40
55.5566
10
. .7716
40
12.34'56
11
7.8936
41
57.8935
11
.9336
41
12.9706
12
8.8888
42
60.2777
12
1.1111
42
13.6111
13
9.9305
43
62.7083
13
1.3040
43
14.2680
14
11.0185
44
65.1852
14
1.5123
44
14.9382
15
12.1527
45
67.7083
15
1.7361
45
15.6250
16
13.3333
46
70.2777
16
1.9763
46
16.3271
17
14.5601
47
72.8935
17
2.2299
47
17.0447
18
15.8333
48
75.6665
18
2.5000
48
17.7777
19
17.1527
49
78.2638
19
2.7856
49
18.5262
20
18.5184
50
81.0185
20
3.0864
60
19.2901
21
19.9305
61
83.8192
21
3.4028
51
20.0694
22
21.3888
52
86.6666
22
3.7346
52
20.8641
23
22.8935
53
89.6601
23
4.0818
53
21.6743
24
24.4444
54
92.6000
24
4.4444
54
22.5000
25
26.0416
55
95.4861
25
4.8228
55
23.3410
26
27.6851
56
98.5185
26
6.2160
56
24.1975
27
29.3750
57
101.5973
27
5.6250
67
25.0694
28
31.1111
68
104.7222
28
6.0494
68
25.9567
29
32.8935
59
107.8935
29
6.4891
59
26.8695
30
34.7222
60
111.1111
30
6.9444
60
27.7777
( Ivi. )
BASE 25 SLOPE
1^ to 1.
1
Add.
•s
Add.
533
Dednct.
".a
SB
Deduct.
s
a:
a
Q
1
.4906
31
4i:0464
1
.0092
31
8.8981
2
1.0370
32
43.2592
2
.0370
32
9.4816
3
1.6389
33
45.5278
3
.0833
33
10.0833
4
2.2964
34
47.8518
4
.1480
34
10.7037
6
3.0092
35
50.2314
5
.2313
36
11.3425
6
3.7777
36
62.6666
6
.3333
36
12.0000
7
4.6016
37
55.1572
7
.4537
37
12.6759
8
5.4814
38
57.7037
8
.5926
38
ia3703
9
6.4166
39
60.3055
9
.7500
39
14.0833
10
7.4073
40
62.9629
10
.9259
40
14.8148
11
8.4538
41
65.6759
11
1.1203
41
15.5648
12
9.5555
42
69.4444
12
1.3333
42
16.3333
13
10.7129
43
71.2685
13
1.5648
43
17.1202
14
11.9259
44
74.1481
14
1.8148
44
17.9259
15
13.1944
45
77.0833
15
2.0833
45
18.7500
16
14.5185
46
80,0740
16
2.3704
46
19.5925
17
16.8981
47
83.1202
17
2.6759
47
20.4637
18
17.3333
48
86.2222
18
3.0000
48
21.3333
19
18.8240
49
89.3794
19
3.3^26
49
22.2314
20
20.3703
50
92.5926
20
3.7037
50
23.1481
21
21.9722
51
95.8611
21
4.0833
61
24.0833
22
23.6296
52
99.1851
22
4.4815
62
25.0370
23
25.3426
53
102.5647
23
4.8981
63
26.0092
24
27.1111
54
106.0000
24
6.3333
54
27.0000
25
28.9350
55
109.4906
25
5.7869
55
28.0092
26
30.8147
56
113.0370
26
6.2692
66
29.0370
27
32.7500
67
116.6389
27
6.7500
57
30.0833
28
34.7407
58
120.2962
28
7.2692
68
31.1481
29
36.7870
59
124.0092
29
7.7869
59
32.2314
30
38.8888
60
127.7777
30
8.3333
60
33.3333
( IvH- )
BASE 26— SLOPE If to 1.
•«->
Add.
1
•8
Add.
if. of
Hts.
Deduct.
if. of
Elts.
Deduct.
a
s
O
Q
1
.4952
31
45.^52
1
.0108
31
10.3811
2
1.0556
32
48.0000
2:
.0432
%
11.0617
S
1.6806
33
60.5696
3
.0972
33
11.7638
4
2.3704
34
63.2037
4
,1728
34
12.4876
6
3.1250
35
56.9027
6
.2700
35
13.2380
6
3.9444
36
68.6666
6
.3889
36
140000
7
4.8284
37
61.4952
7
.5293
37
14.7885
8
6.7777
38
64.3888
8
.6913
38
16.5987
9
6.7916
39
67.3471
9
.8750
39
16.4306
10
7.8702
40
70.3703
10
1.0802
40
17.2839
11
9.0140
41
73.4583
11
1.3071
41
18.1689
12
10.^222
42
77.611]
12
1.6565
^
19.0665
13
11.4962
43
79.8286
13
1.8266
43
19.9747
14
12.8333
44
83.1111
14
2.1173
44
20.9136
16
142361
45
86.4683
16
2.4305
45
21.8750
16
16.7037
46
89.8703
16
2.7664
46
22.8680
17
17.2361
47
93.3471
17
3.1219
47
23.8626
18
ia8333
48
96.8888
18
3.5000
48
24.8888
19
20.4952
49
100.4962
19
a8997
49
25.9367
20
22.2222
60
104.1666
20
4.3210
50
27.0061
21
24.0140
61
107.9027
21
47639
61
28.0972
22
25.8702
62
111.7037
22
6.2284
62
29.2098
23
27.7916
63
115.5696
23
6.7146
63
30.3441
24
29.7777
64
119.6000
24
6.2222
64
31.6000
23
31.8284
65
123.4962
26
&7616
65
32.6774
26
33.9444
66
127.6566
26
7.3024
66
33.8765
27
36.1250
57
131.ffi06
27
7.8750
67
35.0972
28
38.3704
58
136.8703
28
S.4691
68
36.3394
29
40.6806
59
140.1250
29
9.0848
69
37.6033
30
43.0556
60
144.4444
30
9.7222
60
I
38.8888
( Iviii. )
BASE 26— SLOPE 2 to 1.
•8
Add.
1
•8
Add.
if. of
Hts.
Deduct
if. of
Hts.
Dedmct.
a
n
O
«
1
.6000
31
49.9444
1
.0123
31
11.86^
2
1.0740
32
82.7407
2
.0494
32
12.6419
3
1.7222
33
66.6111
3
.1111
33
13.4444
4
2.4444
34
68.6656
4
.1976
34
142716
6
3.2407
36.
61.6740
6
.3086
36
15.1234
6
4.1111
96
64.6666
6
.,4444
36
laoooo
7
6.0666
37
67.8333
7
.6049
37
16.9012
8
6.0740
38
71.0740
8
.7901
38
17.8271
9
7.1666
39
74.3888
9
1.0000
39
18.7777
10
8.3333
40
77.7777
10
1.2346
40
19.7630
11
9.6741
41
81.2407
11
1.4938
41
20.7530
12
10.8888
^
86.7777
12
1.7778
42
21.7777
13
12.2777
43
88.3888
13
2.0864
43
22.8271
14
13.7407
44
92.0740
14
2.4197
44
23.9012
16
14.2777
46
95.8333
16
2.7778
46
26.0000
16
16.8888
46
99.6666
16
3.1606
46
26.1234
17
18.6741
47
103.5740
17
3.5679
47
27.2716
18
20.3333
48
107.6565
18
40000
48
28.4444
19
22.1666
49
111.6111
19
4.4568
^
29.6420
20
240740
60
115.7407
20
49382
50
30.8642
21
26.0556
61
119.9444
21
5.4444
61
32.1111
22
28.1111
62
1242222
22
6.9763
52
33.3827
23
30.2407
63
128.6740
23
&6309
63
34.6790
24
32.4444
64
133.0000
24
7.1111
64
36.0000
25
34.7222
66
137.6000
26
7.7160
66
37.3466
26
37.0740
66
142.0740
26
8.3467
66
38.7160
27
39.5000
67
146.7222
27
9.0000
67
40.1111
28
42.0000
68
161.4444
28
9.6790
58
41.6308
29
44.5740
69
156.2407
29
10.3827
69 42.9763
30
47.2222
60
161.1111 1 30
11.1111
60 44.4444
(liz.)
BASE 25— SLOPE 1^ to 1.
1.
•s
Add.
1
Add.
if. of
Hts.
Dednct.
if. of
Deduct.
K
K
O
Q
1
.5092
31
58.8^5
1
.0154
31
148302
2
1.1111
32
62.2222
2
.0617
32
16.8013
3
1.8065
33
66.6944
3
.1389
33
16.8056
4
2.5926
34
69.2692
4
.2468
34
17.8306
5
3.4722
36
72.9166
5
.3857
36
18.9043
6
4.4444
36
76.6666
6
.5556
36
20.0000
7
5.5092
37
80.5092
7
.7561
37
21.1265
8
6.6666
38
844444
8
.9876
38
22.2839
9
7.9166
39
88.4722
9
1.2500
39
23.4722
10
9.2592
40
92.8386
10
1.64^
40
246913
11
10.6944
41
96.8055
11
1.8673
41
26.9413
12
12.2222
^
101.1111
12
2.2222
42
27.2222
13
13.8425
43
105.6092
13
2.6080
43
28.5360
14
15.5555
44
110.0000
14
a0247
44
29:8765
15
17.3611
46
1145833
15
3.4722
45
31.2600
16
19.2592
46
119.2592
16
3.9506
46
32.6543
17
21.2500
47
124.0277
17
44599
47
340895
18
23.3333
48
128.8888
18
5.0000
48
36.6665
19
25.6092
49
133.8^6
19
5.5710
49
37.0524
20
27.7777
50
138.8888
20
&1728
50
38.6802
21
30.1388
51
144.0277
21
6.8066
51
40.1388
22
32.6926
52
1^.2692
22
7.4691
62
41.7283
23
35.1388
53
1545833
23
8.1636
53
43.3487
24
37.7777
64
160.0000
24
8.8889
54
46.0000
25
40.6092
55
165.6092
25
9.6455
55
46.6820
26
43.3333
66
171.1111
26
10.4321
66
48.3960
27
46.2500
67
176.8055
27
11.2500
57
60.1388
28
49.2692
58
182.5926
28
12.0587
68
51.9136
29
62.3611
59
188.4722
29
12.9782
59
53.7191
30
65.6556
60
1944444
30
13.8889 1 60
65.6555
•
(1x0
BASE 25— SLOPE 3 to 1.
1
Add.
}
Add.
Deduct.
Bednct.
1
m
1
Q
.5185
31
67.7407
.0185
31
17.7963
2
1.1482
32
71.7037
2
.0740
32
18.9630
3
1.8888
33
75.7777
8
.1667
33
2ai666
4
2.7407
34
79.9629
4
.2968
34
21.4074
5
3.7037
35
84.2692
5
.4628
36
22.6851
6
4.7777
36
8a6666
6
.6667
36
24.0000
7
5.9629
37
93.1850
7
.9074
37
25.3518
8
7.2592
38
97.8148
8
1.1852
38
2a7407
9
8.6666
39
102.5655
9
1.5000
39
28.1666
10
10.1851
40
107.4074
10
1.8518
40
29.6296
11
11.8148
41
112.3703
11
2.2407
41
31.1296
12
13.5555
^
117.4444
12
2.6667
4i
32.6666
13
16.4074
43
122.6296
13
3.1296
43
34.2407
14
17.3703
44
127.9258
14
3.6296
44
35.8518
15
19.4444
45
133.3333
15
41667
45
37.6000
16
21.^96
46
138.8518
16
47407
46
39.1861
17
23.9259
47
1444814
17
5.3518
47
40.9074
18
26.3333
48
150.2222
18
6.0000
48
^6666
19
28.8518
49
156.0740
19^
6.6852
49
44.4629
20
31.4815
50
1&LOS70
20
7.4074
50
46.2963
21
34.2222
51
168.1111
21
8.1667
51
49.1666
22
37.0740
52
1742962
22
8.9629
52
50.0740
23
40.0370
53
180.5926
23
9.79^
53
62.0185
24
43.1111
54
187.0000
24
10.6667
54
64.0000
25
46.2962
55
193.5185
25
11.5741
55
66.0184
26
49.5926
56
200.1481
26
12.5184
66
68.0740
27
53.0000
57
206.8888
27
13.6000
57
60.1666
28
56.5185
58
213.7407
28
14.5185
68
62.2962
29
60.1482
59
220.7037
29
15.5741
69
64.4629
30
63.8888
60
227.7777
30
16.6667
60
66.6666
(Ixi.)
BASE 26— SLOPE J to 1.
}
Add.
1
Add.
Deduct.
"S
Deduct.
»
Si
1
o"
1
.4861
31
19.3750
.0015
31
1.4830
2
.9814
32
20.1481
2
.0062
32
1.6802
3
1.4861
33
20.9305
3
.0139
33
1.6806
4
2,0000
34
21.7222
4
.0246
34
1.7839
5
2.5231
35
22.5231
5
.0385
35
1.8904
6
3.0556
36
23.3333
6
.0555
36
2.0000
7
3.6972
37
24.1527
7
.0766
37
2.1126
8
4.1481
38
24.9814
8
.0988
38
2.2284
9
47083
39
25.8194
9
.1250
39
2.3472
10
5.2777
40
26.6666
10
.1543
40
2.4691
11
6.8664
41
27.5231
11
.1867
41
2.5941
12
6.4444
42
28.3888
12
.2222
42
2.7222
13
7.0416
43
29.2638
13
.2608
43
2.8545
14
7.6481
44
30.1481
14
.3025
44
2.9876
15
8.2638
45
31.0416
15
.3472
45
3.1250
16
8.8888
46
31.9444
16
.3961
46
3.2654
17
9.6231
47
32.8564
17
.4460
47
3.4089
18
10.1666
48
33.7777
18
.6000
48
3.6666
19
10.8194
^
34.7083
19
.6.571
49
3.7062
20
11.4814
60
36.6481
20
.6173
60
3.8580
21
12.1627
51
36.6972
21
.6806
51
4.0139
22
12.8333
52
37.5655
22
.7469
52
4.1728
23
13.5231
63
S8.£@3l
23
.8163
63
4.3349
24
14.2222
64
39.6000
24
.8889
64
46000
25
14.9306
55
40.4861
25
.9647
66
4.6682
26
16.6481
56
41.4814
26
1.0432
66
48395
27
16.3760
57
42.4861
27
1.1260
67
6.0139
28
17.1111
68
43.6000
28
1.2099
68
5.1913
29
17.8664 1 69
44.6231
29
1.2978
69
6.3719
30
18.6111 1 60
45.5556
30
1.3889
60
5.5655
( I'^ii- )
BASE 26— SLOPE i to 1.
1
Add.
**
Add.
Deduct.
Dednct.
n
1
n
31
1
Q*
.4907
23.8241
.0031
31
2.9660
2
1.0000
32
24.8888
2
.0123
32
3.1606
8
1.6277
33
25.9722
3
.0278
33
3.3611
4
2.0741
34
27.0740
4
.0494
34
8.5679
6
2.6388
36
28.1944
5
.0772
36
3.7808
6
a2222
36
29.3333
6
.1111
36
4.0000
7
3.8240
37
30.4908
7
.1512
37
4.2253
8
4.4444
38
31.6666
8
.1976
38
4.4668
9
6.0833
39
32.8611
9
.2600
39
4.6944
10
6.7407
40
34.0740
10
.3086
40
4.9383
11
6.4166
41
35.3056
11
.3734
41
5.1883
12
7.1111
42
36.5665
12
.4444
^
6.4444
13
7.8240
43
37.8240
IS
.6216
43
6.7067
14
8.5665
44
39.1111
14
.6049
44
5.9763
16
9.3054
45
40.4166
16
.6944
46
6.2600
16
10.0740
46
41.7407
16
.7901
46
6.6308
17
10.8611
47
43.0833
17
.8920
47
&8179
18
11.6666
48
44.4444
18
1.0000
48
7.1111
19
12.4907
49
45.8240
19
1.1142
49
7.4105
20
13.3333
50
47.2222
20
1.2346
50
7.7160
21
14.1944
51
48.6388
21
1.3611
61
8.0277
22
15.0740
62
60.0740
22
1.4938
52
8.3456
23
15.9722
63
61.5277
23
1.6327
63
8.6697
24
16.8888
64
53.0000
24
1.7778
54
9.0000
25
17.8240
66
64.4907
2g
1.9296
66
9.3364
26
18.7777
56
56.0000
26
2.0864
66
9.6790
27
19.7500
57
57.6277
27
2.2600
57
10.0277
28
20.7407
58
69.0740
28
2.4197
58-
10.3827
29
21.7500
59
60.6388
29
2.6956
59
10.7438
30
22.7777
60
62.2222
30
2.7778
60
11.1111
( Ixiii. )
BASE 26— SLOPE f to 1.
1
*
Add.
1
Add.
Deduct.
Deduct.
»
»
1
a"
1
.^53
31
28.2732
.0046
31
44490
2
1.0185
32
29.6296
2
.0186
32
47407
3
1.5694
33
31.0139
3
.0416
33
6.0416
4
2.1481
34
32.4258
4
.0740
34
5.3518
5
2.7545
35
33.8657
5
.1167
35
5.6712
6
3.3888
36
35.3333
6
.1667
36
6.0000
7
4.0508
37
36.8287
7
,2268
37
6.3379
8
4.7407
38
38.3518
8
.2963
38
6.6851
9
5.4583
39
39.9027
9
.3750
39
7.0416
10
6.2036
40
41.4814
10
.4630
40
7.4074
11
&9768
41
43.0680
11
.6602
41
7.7824
12
7.7777
42
44.7222
12
.6667
^
8.1666
13
8.6064
43
46.3842
13
.7824
43
8.6602
14
9.4629
44
48.0740
14
.9074
44
8.9629
16
10.3470
45
49.7916
15
1.0417
45
9.3760
16
11.2592
46
51.6370
16
1.1862
46
9.7962
17
12.1990
47
53.3101
17
1.3379
47
10.2268
18
13.1666
48
56.1111
18
1.6000
48
10.6666
19
141620
49
56.9397
19
1.6713
49
11.1157
20
15.1851
50
68.7962
20
1.8518
60
11.6740
21
16.2360
51
60.6806
21
2.0417
51
12.0416
22
17.3147
52
62.6926
22
2.2407
62
12.6185
23
18.4213
53
64.5322
23
2.4491
63
13.0046
24
19.5555
54
66.5000
24
2.6667
64
13.5000
25
20.7175
55
68.4952
25
2.8936
56
14.0046
26
21.9073
56
70.6186
26
3.1296
56
14.6185
27
23.1250
57
72.6694
27
3.3760
57
15.0416
28
243703
58
74.6481
28
3.6296
68
15.5740
29
25.6435
59
76.7646
29
a8935
69
16.1167
30
26.9444
60
78.8888
30 416671
60
1&6666
( l«v. )
BASE 26— SLOPE 1 to 1.
1
•8
Add.
1
Add.
"a
•
Deduct.
3^
Deduct.
M
a
fi"
fi
1
.6000
81
32.7222
1
.0062
31
6.9321
2
1.0370
82
84.8703
2
.0247
82
6.821U
8
1.6111
38
86.0555
8
.0566
33
6.7222
4
2.2222
84
37.7777
4
.0988
84
7.1858
6
2.8704
86
89.5370
5
.1643
85
7.5617
6
3.6656
36
41.3388
6
.2222
86
8.0000
7
4.2777
87
43.1666
7
.8025
37
8.4506
8
6.0870
38
46.0370
8
.3951
38
&9135
9
5.8338
89
46.9444
9
.6000
89
9.3888
10
6.6666
40
48.8888
10
.6173
40
9.8765
11
7.5870
41
50.8704
11
.7469
41
10.8766
12
8.4444
^
62.8888
12
.8889
42
10.8888
13
9.3888
43
64.9444
18
1.0432
48
11.4135
14
10.8703
44
67.0370
14
1.2099
44
11.9506
16
11.8888
45
59.1666
15
1.3889
45
12.6000
16
12.4444
46
61.8333
16
1.6802
46
13.0617
17
13.6370
47
63.5870
17
1.7839
47
13.6358
18
14.6666
48
65.7777
18
2.0000
48
14.2222
19
16.8333
49
68.0565
19
2.2284
^
14.8209
20
17.0370
50
70.8703
20
2.4691
60
15.4321
21
18.2777
61
72.7222
21
2.7222
61
16.0556
22
19.6565
52
76.1111
22
2.9876
52
16.6913
23
20.8704
63
77.5870
23
3.2654
63
17.3395
24
22.2222
54
80.0000
24
3.6656
54
18.0000
25
23.6)11
56
82.6000
25
3.8680
56
18.6728
26
26.0370
66
85.0870
26
4.1728
66
19.3580
27
2&6000
57
87.6111
27
46000
67
20.0556
28
28.0000
68
90.2222
28
4.8395
58'
20.7664
29
29.5370
69
92.8704
29
5.1913
59
21.4876
30
31.1111
60
96.5556
30
6.6566 60
22.2222
( Ixv. )
"
BASE 26— SLOPE IJ to L
1
Add.
1
Add.
"a
Deduct.
an
Deduct.
n
K
.
o"
O*^
1
.5046
31
37.1713
1
.0077
31
7.4151
2
1.0555
32
39.1111
2
.0309
32
7.9012
3
1.6528
33
41.0972
3
.0694
33
&4027
4
2.2963
34
43.1296
4
.1234
34
8.9197
5
2.9859
35
45.2083
6
.1928
36
9.4621
6
3.79912
36
47.3333
6
,2778
36
10.0000
7
45045
87
49.5046
7
.3781
37
10.5632
8
5.3333
38
61.7222
8
.4938
38
11.1419
9
6.2083
39
53.9860
9
.6250
39
11.7361
10
7.1296
40
56.2962
10
.7716
40
12.3456
11
8.0972
41
68.6628
11
.9336
41
12.9706
12
9.1111
42
61.0565
12
Llill
42
13.6111
13
10.1712
43
63.5046
13
1.3040
43
142680
14
11.2777
44
66.0000
14
1.5123
44
14.9382
15
12.4304
45
68.5416
15
1.7361
45
15.6250
16
13.6296
46
71.1296
16
1.9763
46
ia3271
17
14.8760
47
73.7639
17
2.2299
47
17.0447
18
16.1666
48
76.4444
18
2.5000
48
17.7777
19
17.5046
49
. 79.1712
19
2.7856
49
18.6262
20
18.8888
50
81.9444
20
3.0864
60
19.2901
21
20.3196
61
84.7639
21
a4028
61
20.0694
22
21.7962
52
87.6296
22
3.7346
62
20.8641
23
23.3195
53
90.6416
23
4.0818
53
21.6743
24
24.8888
54
93.5000
24
4.4444
54
22.5000
25
26iK)46
65
96.5046
25
4.6228
55
23.3410
26
28.1666
66
99.5555
26
5.2160
56
241976
27
29.8750
67
102.6528
27
5.6260
57
25.0694
28
31.6296
68
105.7962
28
6.0494
58
25.9667
29
33.4306
69
108.9860
29
6.4891
59
26.8696
30
86.2777
60
112.2222
30
6.9444
60
K
27.7777
( IxTi. )
BASE 26— SLOPE 1^ to 1.
1
•8
Add. -e
Add.
Dednct.
Dednct.
M
»
q"
f^ p*4
1
.5092
31
41.6204
1
.0092
31
8.8981
2
1.0740
32
43.8618
2
.0870
32
9.4815
3
1.6944
33
46.1389
3
.0833
38
10.0838
4
2.8704
34
48.4815
4
.1480
84
10.7037
5
3.1016
35
50.8796
5
.2313
36
11.3425
6
3.8888
36
53.3333
6
.3338
36
12.0000
7
4.7314
37
55.8424
7
.4637
37
12.6769
8
5.6296
38
58.4074
8
.5926
38
13.3703
9
6.5833
39
61.0277
9
.7500
39
14.0833
10
7.5926
40
63.7037
10
.9259
40
148148
11
8.6574
41
66.4362
11
1.1203
41
15.5648
12
9.7777
42
70.2222
12
1.3333
42
16.3333
13
10.9536
43
72.0648
13
1.6648
48
17.1202
14
12.1851
44
74.9629
14
1.8148
44
17.9259
15
13.4720
45
77.9166
15
2.0833
45
18.7600
16
148148
46
80.9260
16
2.3704
46
19.5925
17
16.2129
47
83.9907
17
2.6769
47
20.4537
18
17.6666
48
87.1111
18
3.0000
48
21.3833
19
19.1759
49
90.2870
19
3.3426
49
22.2314
20
20.7407
50
93.6185
20
3.7037
50
28.1481
21
22.8611
51
96.8065
21
40838
61
24.0833
22
24.0370
52
100.1481
22
44815
52
26.0370
23
25.7686
53
103.5462
23
48981
53
26.0092
24
27.6565
64
107.0000
24
5.3383
54
27.0000
25
29.3981
65
110.6092
26
5.7869
66
28.0092
26
31.2962
56
1140740
26
6.2592
66
29.0370
27
83.2500
67
117.6945
27
6.7600
67
30.0833
28
35.2592 58
121.8704
28
7.2692
58
31.1481
2d
37.3240 69
126.1017
29
7.7869
59
32.2314
80 39.44441 60
128.8888
30
8.3833
60
33.3333
( Ixvii. )
BASE 26— SLOPE If to 1.
1
Add.
1
•s
Add.
Deduct.
"Sri
Dedoct.
1
s
O*
o"
.5138
31
46.0694
1
.0108
31
10.3811
2
1.0926
32
48.5926
2
.0432
32
11.0617
3
1.7361
33
51.1805
3
.0972
.33
11.7638
4
2.4444
34
63.8333
4
.1728
34
12.4876
6
3.2176
35
56.6509
5
.2700
35
ia2330
6
4.0555
86
69.3333
6
.3889
36
14.0000
7
4.9582
37
62.1805
7
.5293
37
147885
8
5.9259
38
65.0926
8
.6913
38
15.5987
9
&9582
39
68.0694
9
.8750
39
16.4305
10
8.0555
40
71.1111
10
1.0802
40
17.2839
11
9.2176
41
74.2176
11
1.3071
41
18.1589
12
10.4444
42
78.3888
12
1.5556
42
19.0556
13
11.7361
43
80.^50
13
1.8266
43
19.9747
14
13.0926
44
83.9258
14
2.1173
44
20.9135
15
14.5138
46
87.2916
15
2.4306
45
21.8750
16
16.0000
46
90.7222
16
2.7654
46
22.8580
17
17.5508
47
94.2177
17
3.1219
47
23.8626
18
19.1666
48
97.7777
18
3.6000
48
24.8888
19
20.8472
49
101.4026
19
3.8997
49
26.9367
20
22.6926
50
106.0926
20
4.3210
50
27.0061
21
24.4026
51
108.8472
21
4.7639
51
28.0972
22
26.2777
62
112.6666
22
5.2284
52
29.2098
23
28.2177
53
116.5608
23
5.7145
53
30.3441
24
30.2222
54
120.51K)0
24
6.2222
64
31.5000
25
32.2916
65
124.5138
25
6.7516
56
32.6774
26
34.4258
56
128.5926
26
7.3024
66
33.8765
27
36.6250
57
182.7361
27
7.8750
57
35.0972
28.
.38.8888
58
136.9444
28
8.4691
68
36.3394
29
41.2176
69
141.2174
29
9.0848
59
37.6033
30
43.6111
60
145.6555
30
9.7222
1 60
38.8888
( Ixviii. )
BASE 26— SLOPE 2 to 1.
Add.
1 .5185
2 1.1111
3 1.7777
4 2.5185
5 3.3333
6 4.2222
7 5.1851
8 6.2222
9 7.3333
10 8.5185
11 9.7777
12 11.1111
13 12.5185
14 i4.oooa
15 15.5555
16 17.1851
17 18.8888
18 20.6666
19 22.5185
24.4444
20
21
22
23
24
25
26
27
28
29
30
26.4444
28.5185
30.6666
32.8888
35.1851
37.5555
40.0000
42.5185
45.1111
47.7777
•t
Add.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
67
58
59
60
50.5185
53.3333
56.2222
59.1851
62.2222
65.3333
68.5185
71.7777
75.1111
78.5185
82.0000
86.5555
89.1851
92.8888
96.6666
100.5185
104.4444
108.4444
112.5185
116.6666
120.8888
125.1851
129.5555
134.0000
138.5185
143.1111
147.7777
152.5185
157.3333
162.2222
• a
1
•2
8
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22.
23
24
25
26
27
28
29
SO
Deduct.
.0123
.0494
.1111
.1975
.3086
A444
• A X M. X
.6049
.7901
1.0000
1.2346
1.4938
1.7778
2.0864
2.4197
2.7778
3.1605
3.5679
4.0000
4.4568
4.9382
5.4444
5.9753
6.5309
7.1111
7.7160
8.3457
9.0000
9.6790
10.3827
11.1111
o j5*
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
61
52
53
54
55
56
57
58
59
60
Deduct.
11.8642
12.6419
13.4444
14.2716
15.1234
16.0000
16.9012
17.8271
18.7777
19.7530
20.7530
21.7777
22.8271
23.9012
25.0000
26.1234
27.2716
28.4444
29.6420
30.8642
32.1111
33.3827
34.6790
36.0000
37.3456
38.7160
40.1111
41.5308
42.9753
AA AAAA
XX. X X XX
( Ixix, )
BASE 26— SLOPE 2J to 1.
1
Add.
i
Add.
Dif. of
Hts.
Deduct.
Deduct.
1
.5277
31
59.4166
1
.0154
31
14.8302
2
1.1482
32
62.8148
2
.0617
32
16.8016
3
1.8611
33
66.3055
3
.1389
33
16.8066
4
2.6666
34
69.8888
4
.2468
34
17.8395
5
3.5648
35
73.5648
6
.3857
35
18.9043
6
4.5555
36
77.3333
6
.5665
36
20.0000
7
5.6388
37
81.1944
7
.7661
37
21.1265
8
6.8148
38
85.1482
8
.9876
38
22.2839
9
8.0833
39
89.1944
9
1.2500
39
23.4722
10
9.4444
40
93.3333
10
1.5432
40
24.6913
11
10.8981
41
97.5648
11
1.8673
41
25.9413
12
12.4444
42
101.8888
12
2.2222
42
27.2222
13
14.0833
43
106.3055
13
2.6080
43
28.5360
14
15.8148
44
110.8148
14
3.0247
44
29.8765
16
17.6388
46
116.4166
16
a4722
46
31.2500
16
19.5555
m
120.1111
16
3.9506
m
32.6543
17
21.5648
47
124.8981
17
4.4699
47
34.0896
18
23.0666
48
129.7777
18
6.0000
48
36.6665
19
25.8611
49
134.7600
19
5.6710
49
37.0524
20
28.1482
50
139.8148
20
6.1728
50
38.6802
21
30.6277
61
144.9722
21
6.8066
51
40.1388
22
33.0000
52
150.3222
22
7.4691
62
41.7283
23
36.5648
63
165.5648
23
8.1636
63
43.3487
24
38.2222
54
161.0000
24
8.8889
64
46.0000
25
40.9722
56
166.6277
25
9.6466
55
46.6820
26
43.8148
56
172.1482
26
10.4321
66
48.3950
27
46.7500
57
177.8611
27
11.2500
67
50.1388
28
49.7777
68
183.6666
28
12.0687
68
51.9135
29
52.8981
59
189.6648
29
12.9782
59
63.7191
30
56.1111
60
196.5566
30
13.8889
60
56.6556
( 1«. )
BASE 26— SLOPE 3 to 1.
*
Add.
4^
t
Add.
«4M
Deduct.
"a
Deduct.
1
as
o
a
.6370
31
68.3148
1
.0186
31
17.7963
2
1.1852
32
72.2962
2
.0740
32
18.9630
3
1.9444
33
76.3888
3
.1667
33
20.1666
4
2.8148
34
80.6926
4
.2963
34
21.4074
5
3.7962
35
84.9074
5
.4628
35
22.6851
6
4.8888
36
89.3333
6
.6667
36
240000
7
6.0926
37
93.8703
7
.9074
37
25.3618
8
7.4074
38
98.6186
8
1.1862
38
26.7407
9
8.8333
39
103.2777
9
1.6000
39
28.1666
10
10.3703
40
108.1481
10
1.8518
40
29.^96
11
12.0186
41
113.1296
11
2.2407
41
31.1296
12
13.7777
42
118.2222
12
2.6667
42
32.6666
13
16.6482
43
123.^259
13
3.1296
43
342407
14
17.6296
44
128.7407
14
3.6296
44
36.8518
16
19.7222
46
134.1666
16
41667
45
37.6000
16
21.9269
46
139.7037
16
47407
46
39.1861
17
24.2407
47
145.3517
17
6.3618
47
40.9078
18
26.6666
48
161.1111
18
6.0000
48
42.6666
19
29.2037
49
156.9814
19
6.6862
49
44.4629
20
31.8618
60
162.9630
20
7.4074
60
46.2963
21
34.6111
51
169.0555
21
8.1667
61
49.1666
22
37.4816
62
176.2692
22
8.9629
62
60.0740
23
40.4630
63
181.5740
23
9.7962
63
62.0185
24
43.6566
54
188.0000
24
10.6667
54
54.0000
26
46.7592
65
1946370
26
11.6741
56
56.0184
26
60.0740
66
201.1861
26
12.6184
66
68.0740
27
53.6000
67
207.9444
27
13.5000
57
60.1666
28
57.0370
68
214.8148
28
145186
68
62.2962
29
60.6861
69
221.7962
29
15.6741
69
64.4629
30
64.4444
60
228.8888
•
30
ia6667
60
66.6666
( Ixxi. )
BASE 27-8LOPE
i to 1.
1
•s
Add.
■^
t
Add.
***
saaa
Deduct.
Deduct.
B
a
o
Q
1
.6046
31
19.9490
1
.0016
31 1.4830
2
1.0186
32
20.7407
2
.0062
32 1.5802
3
1.6416
33
21.6416
3
.0139
33
1.6805
4
2.0740
34
22.3518
4
.0246
34
1.7839
5
2.6167
36
23.1712
6
.0385
35
1.8904
6
3.1666
36
24.0000
6
.0566
36
2.0000
7
3.7268
37
24.8379
7
.0766
37 2.1126
8
4.2962
38
26.6861
8
.0988
38
2.2284
9
4,8760
39
26.6416
9
.1250
39
2.3472
10
6.4629
40
27.4074
10
.1643
40
2.4691
11
&0601
41
28.2824
11
.1867
41
2.5941
12
6.6666
42
29.1666
12
.2222
42
2.7222
13
7.2824
43
30.0601
13
.2608
43
2.8646
14
7.9074
44
30.9629
14
.3025
44
2.9876
16
8.6416
46
31.8750
16
.3472
46
3.1250
16
9.1861
46
32.7962
16
.3951
46
3.2654
17
9.8379
47
33.7268
17
.4460
47
3.4089
18
10.6000
48
34.6666
18
.5000
48
3.6565
19
11.1712
49
36.6167
19
.6571
49
3.7052
20 11.8618
60
36.6740
20
.6173
60
3.8580
21
12.6416
61
37.6416
21
.6805
61
4.0189
22
13.2407
62
38.6186
22
.7469
52
41728
23
13.9400
63
39.6046
23
.8163
63
4.3349
24
14.6666
64
40.6000
24
.8889
64
45000
26
16.3936
66
41.6046
26
.9647
56
46682
26
16.1296
66
42.6186
26
1.0432
56
48396
27
16.8760
67
43.6416
27
1.1250
67
6.0139
28
17.6296
68
44.6740
28
1.2099
58
6.1913
29
18.3936
69
46.6167
29
1.2978 69
6.3719
30
19.1666
60 1 46.6666
30
1.3889 60
5.5666
( Ixxii. )
BASE 27— SLOPE i to 1.
1
Add.
1
•55
Add.
if. of
Hts.
Deduct.
Dif.of
Hts.
Deduct.
a
a:
O
1
.6092
31
24.3981
1
.0031
31
2.9660
2
1.0370
32
26.4814
2
.0123
32
3.3611
3
1.5833
33
26.6833
3
.0278
33
3.6111
4
2.1481
34
27.7037
4
.0494
34
3.5679
d
2.7314
36
28.8426
6
.0772
35
3.7808
6
3.3333
36
30.0000
6
.1111
36
40000
7
3.9536
37
31.1758
7
.1612
37
42253
8
45926
38
32.3703
8
,1976
38
44568
9
5.2500
39
33.6833
9
,2500
39
46944
10
5.9258
40
34.8148
10
.3086
40
49383
11
6.6203
41
36.0648
11
.3734
41
5.1883
12
7.3383
42
37.3333
12
.4444
42
5.4444
13
8.0648
43
38.6203
13
.6216
43
5.7076
14
8.8148
44
39.9268
14
.6049
44
5.9753
15
9.5833
45
41.2500
16
.6944
45
6.2500
16
10.3703
46
42.5926
16
.7901
46
&6308
17
11.1758
47
43.9536
17
.8920
47
6.8179
18
12.0000
48
45.3333
18
1.0000
48
7.1111
19
12.8425
49
46.7314
19
1.1142
49
7.4105
20
13.7037
60
48.1481
20
1.2346
50
7.7160
21
14.5833
61
49.5833
21
1.3611
51
8.02T7
22
15.4814
52
61.0370
22
1.4938
62
8.3466
23
16.3981
53
52.6092
23
1.6327
63
8.6607
24
17.3333
54
540000
24
1.7778
64
9.0000
25
18.2870
65
55,6092
26
1.9296
66
9.3364
26
19.2692
56
67.0370
26
2.0864
56
9.6790
27
20.2500
67
68.5833
27
2.2500
57
10.0277
28
21.2592
68
60.1481
28
2.4197
58
10.3827
29
22.2870
69
61.7314
29
2.6956
59
10.7438
30
23.3333
60
63.3333
30
2.7778
60
11.1111
( Izxiii. )
BASE 27— SLOPE i to 1.
•s
Add.
Add.
Deduct.
3^
Deduct.
X
K
Q
o
1
.5138
31
28.8470
1
.0046
31
4.4490
2
1.0555
32
30.2222
2
.0185
32
4.7407
3
1.6250
33
31.6250
3
.0416
33
5.0416
4
2.2222
34
33.0565
4
.0740
34
5.3518
6
2.8472
35
34.5138
5
.1167
36
5.6712
6
3.5000
36
36.0000
6
.1667
36
6.0000
7
4.1804
37
37.6138
7
.2268
37
6.3379
8
4.8888
38
39.0665
8
.2963
38
&6851
9
5.6250
39
40.6250
9
.3750
39
7.0416
10
6.3888
40
42.2222
10
.4630
40
7.4074
11
7.1805
41
43.8472
11
.5602
41
7.7824
12
8.0000
42
45.5000
12
.6667
42
8.1666
13
8.8472
43
47.1805
13
.7824
43
8.5612
14
9.7222
44
48.8888
14
.9074
44
8.9629
16
10.6250
45
so.eoso
16
1.0417
45
9.3750
16
11.5655
46
52.3888
16
1.1862
46
9.7962
17
12.5138
47
64.1805
17
1.3379
47
10.2268
18
13.5000
48
56.0000
18
1.5000
48
10.6666
19
14.5138
49
57.8472
19
1.6713
49
11.1157
20
15.6555
50
69.7222
20
1.8618
50
11.5740
21
16.6260
51
61.6250
21
2.0417
51
12.0416
22
17.7222
52
63.5555
22
2.2407
52
12.5186
23
18.8472
53
66.6138
23
2.4491
53
13.0046
24
20.0000
54
67.6000
24
2.6667
54
13.5000
25
21.1806
55
69.5138
26
2.8935
55
14.0046
26
22.3888
66
71.5566
26
3.1296
66
14.5185
27
23.6250
57
73.6260
27
3.8760
67
15.0416
28
24.8888
58
75.7222
28
3.6296
58
16.6740
29
26.1804
59
77.8472
29
a8985
66
16.1157
30
27.5000
60
80.0000
30
4.1667
60
16.6666
( Izxiv. )
BASE 27— SLOPE 1 to 1.
t
Add.
1
n
A<M.
Dif.of
Hti.
Deduct.
Dif.of
Hto.
Deduct.
1
.5184
31
33.2962
1
.0062
31
5.9321
3
1,0740
82
84.9629
2
.0247
32
&3210
3
1 £iti£i£t
l.OdQD
33
86.6666
8
.0556
33
ft7222
4
2.2962
84
38.4074
4
.0988
34
7.1368
5
2.9629
35
40.1861
5
.1543
36
7.6617
6
36
42.0000
6
.2222
36
8.0000
7
44074
87
43.8618
7
.3025
37
8.4506
8
5.1851
88
45.7407
8
.3951
38
8.9135
9
&0000
39
47.6666
9
.5000
39
9.3888
10
6.8518
40
49.6296
10
.6173
40
9.8765
11
7.7407
41
51.6296
11
.7469
41
10.3765
12
8.6666
42
53.6666
12
.8889
42
10.88iS8
13
9.6296
43
68.7407
13
1.0432
43
11.4135
14
10.6296
44
67.8618
14
1.2099
44
11.9506
16
11.6666
45
60.0000
15
1.3889
46
13.6000
16
12.7407
46
62.1851
16
1.5802
46
13.0617
17
13.8518
47
64.4074
17
1.7839
47
13.6358
18
15.0000
48
66.6666
18
2.0000
48
142222
19
16.1861
49
68.9629
19
2.2284
49
148209
20
17.4074
50
71.3962
20
2.4691
60
15.4^1
21
18.6666
51
73.6666
21
2.7222
61
16.0555
22
19.9629
m
76.0740
22
2.9876
52
lft6913
23
21.2962
53
78.6184
23
3.2664
63
17.3395
24
22.6666
54
81.0000
24
3.6655
54
18.0000
25
34.0740
65
83.5184
26
3.8630
66
18.6728
26
25.5184
66
86.0740
26
41728
56
19.3680
27
37,0000
67
88.6666
27
46000
67
20.0556
28
28.6184
68
91.2962
28
48395
68
20.7654
39
30.0740
59
93.9629
29
6.1913
59
21.4876
30
31.6666
60
96.6666
•
30
6.5666
60
22.2222
(IXIT. )
BASE 27— SLOPE
1| to 1.
t
Add.
1
•
Add.
if. of
Ht8.
Dedoet.
3^
Deduct.
»
»
Q
Q
1
.5230
31
37.7453
1
.0077
31
7.4161
2
1.0926
32
39.7036
2
.0809
32
7.9012
3
1.7083
33
41.7083
3
.0694
33
8.4027
4
2.3703
34
43.7692
4
.1234
34
8.9197
5
3.0788
35
45.8564
5
.1928
86
9.4521
6
3.8333
36
48.0000
6
.2778
36
10.0000
7
4.6342
37
50.1897
7
.3781
37
10.6632
8
5.4814
38
62.4259
8
.'^38
38
11.1419
9
6.3750
39
64.7083
9
.6250
39
11.7361
10
7.3148
40
57.0870
10
.7716
40
12.3456
11
8.3009
41
69.4120
11
.9386
41
12.9706
12
9.3^3
42
61.8833
12
1.1111
42
18.6111
13
10.4120
43
64.3009
13
1.3040
43
14.2680
14
11.5370
44
66.8147
14
1.6123
44
14.9382
15
12.7082
45
69.3760
16
1.7361
45
15.6250
16
13.9259
46
71.9814
16
1.97SS
46
16J3271
17
15.1897
47
74.6342
17
2.2299
47
17/)447
18
16.6000
48
77.8338
18
2.5000
48
17.7777
19
17.8564
49
80.0788
19
2.7856
49
18JiQ6&
20
19.2592
50
82.8708
20
8.0864
60
1942901
21
20.7083
51
86.7088
21
8.4028
61
20.0694
22
22.2036
52
88.5926
2J
3.7346
BH
20.8641
23
23.7463
53
91.5230 ,
23
4.0818
53
21.6743
24
25.3333
54
94.5000
24
4.4444
54
22.5000
25
26.9675
56
97.5230
26
4.8228
m
23^10
26
26.6480
56
100.6926
26
5.2160
56
24.1976
27
30.3760
67
103.7083
27
5.6250
57
25.0694
28
32.1481
58
106.8708
28
6.0^^4
68
25.9567
29
33.9675
59
110.0788
29
6.4891
59
26.8596
30
35.8333
60
113.8333
30
6.9444
60
27.7777
( Ixxvi. )
BASE 27— SLOPE IJ to 1.
33
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
^^
30
Add.
.5277
1.1111
1.7500
2.4444
3.1944
4.0000
4.8610
5.7777
6.7500
7.7777
8.8610
10.0000
11.1944
12.4444
13.7500
15.1111
16.5277
18.0000
19.5277
21.1111
22.7500
24.4444
26.1944
28.0000
29.8610
31.7777
33.7500
35.7777
37.8610
40.0000
-a
•s
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Add.
42.1944
44.4444
46.7500
49.1111
51.5277
54.0000
56.5277
59.1111
61.7500
64.4444
67.1944
70.0000
72.8610
75.7777
78.7500
81.7777
84.8610
88.0000
91.1944
94.4444
97.7500
101.1111
104.5277
108.0000
111.5277
115.1111
118.7500
122.4444
126.1944
130.0000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Deduct.
.0092
.0370
.0833
,1480
.2313
.3333
.4537
.5926
.7500
.9259
1.1203
1.3333
1.5648
1.8148
2.0833
2.3704
2.6759
3.0000
3.3426
3.7037
4.0833
4.4815
4.8981
5.3333
5.7869
6.2592
6.7500
7.2592
7.7869
8.3333
^5
s
Deduct.
31 8.8981
32 9.4815
33 10.0833
34 10.7037
35 11.3425
36 12.0000
37 12.6759
38 13.3703
39 14.0833
40 14.8148
41 15.5648
42 16.3333
43 17.1202
44 17.9259
45 18.7500
46 19.5925
47 20.4537
48 21.3333
49 22.2314
50 23.1481
51 24.0833
52 25.0370
53 26.0092
54 27.0000
55 28.0092
56 29.0370
57 30.0833
58 31.1481
59 32.2314
60 33.3333
•
( Ixxvii. )
BASE 27— SLOPE
1* to 1.
1
»
Add.
i
Add.
1
Deduct.
Dif. of
Hts.
Deduct.
1
.5323
31
46.6435
.0108
31
10.3811
2
1.1296
32
49.1851
2
.0432
32
11.0617
3
1.7916
33
51.7916
3
.0972
33
11.7638
4
2.5185
34
54.4629
4
.1728
34
12.4876
5
3.3101
35
67.1990
5
.2700
36
13.2330
6
4.1666
36
60.0000
6
.3889
36
14.0000
7
5.0878
37
62.8636
7
.5293
37
14.7886
8
6.0740
38
66.7962
8
.6913
38
16.6987
9
7.1250
39
68.7916
9
.8760
39
16.4305
10
8.2406
40
71.8518
10
1.0802
40
17.2839
11
9.4213
41
74.9768
11
1.3071
41
18.1689
12
10.6666
42
78.1666
12
1.6566
42
19.0556
13
11.9768
43
81.4212
13
1.8256
43
19.9747
14
13.3518
44
84.7407
14
2.1173
44
20.9136
16
147916
45
88.1260
15
2.4305
45
21.8750
16
16.2962
46
91.6740
16
2.7654
46
22.8580
17
17.8666
47
95.0878
17
3.1219
47
23.8326
18
19.6000
48
98.6666
18
3.5000
48
24.8888
19
21.1990
^
102.3101
19
3.8997
49
25.9367
20
22.9629
50
106.0185
20
4.3210
50
27.0061
21
24.7916
51
109.7916
21
4.7639
51
28.0972
22
26.6851
52
113.6296
22
6.2284
52
29.2098
23
28.6436
63
117.5323
23
5.7145
53
30.3441
24
30.6666
54
121.5000
24
6.2222
54
31.6000
23
32.7645
55
126.5323
26
6.7616
55
32.6774
26
34.9073
56
129.6296
26
7.3024
56
33.8765
27
37.1250
67
133.7916
27
7.8750
57
35.0972
28
39.4073
68
138.0185
28
8.4691
68
36.3394
29
41.7545
69
142.3101
29
9.0848
69
37.603&
30
44.1666
60
146.6666
30
9.7222
60
38.8888
( IxxTiii. )
•
BASE 27-8LOPE 2 to 1.
i-> Height
Add.
1
s
Add.
1
Deduct
Dif.of
HtB.
Deduct.
.6370
31
51.0926
.0123
31
11.8642
2
1.1481
32
63.9268
2
.0494
32
12.6419
3
1.8333
33
56.8333
3
.1111
33
13.4444
4
2.5926
34
59.8147
4
.1975
34
142716
6
3.4258
35
62.8703
6
.3086
35
16.1234
6
4.3333
36
66.0000
6
.4444
36
16.0000
7
5.3148
37
69.2037
7
.6049
37
16.9012
8
6.3703
38
72.4814
8
.7901
38
17.8271
9
7.6000
39
76.8333
9
1.0000
39
18.7777
10
8.7037
40
79.2592
10
1.2346
40
19.7530
11
9.9816
41
82.7692
11
1.4938
41
20.7530
12
11.3333
42
86.3333
12
1.7778
42
21.7777
13
12.7692
43
89.9814
13
2.0864
43
22.8271
14
14.2692
44
93.7037
14
2.4197
44
23.9012
15
16.8333
45
97.6000
15
2.7778
45
25.0000
16
17.4815
46
101.3708
16
3.1605
46
26.1234
17
19.2037
47
105.3147
17
3.5679
47
27.2716
18
21.0000
48
109.3333
18
40000
48
28.4444
19
22.8703
49
113.4258
19
44568
49
29.6420
20
248148
60
117.6926
20
49382
50
30.8642
21
26.8333
51
121.8333
21
5.4444
51
32.1111
22
289258
62
126.1480
22
5.9753
62
33.3827
23
31.0926
63
130^870
23
6.6309
53
346790
24
33.3333
54
136.0000
24
7.1111
64
36.0000
25
36.6480
66
139.6370
25
7.7160
66
37.3456
26
38.0370
66
144.1480
26
8.3457
56
38.7160
27
40.6000
67
148.8333
27
9.0000
57
40.1111
28
43.0370
68
153.5926
28
9.6790
68
41.6308
29
46.6480
59
158.4268
29
10.3827
69
42.9763
SO
48.3333
60
163.3333
30
11.1111
60
444444
( Izxix. )
BASE 27 SLOPE 2| to 1.
1
Add.
1
n
Add.
Dif. of
HtB.
Deduct.
Dif. of
Hto.
Deduct.
1
.5462
31
59.9908
1
.0154
31
148302
2
1.1851
32
63.4073
2
.0617
32
15.8013
3
1.9166
33
66.9166
3
.1389
33
1&8066
4
2.7408
34
70.5186
4
.2468
34
17.8895
6
3.6573
35
742129
5
.3857
35
18.9043
6
4.6666
36
78.0000
6
.5556
36
20.0000
7
5.7686
37
81.8796
7
.7661
37
21.1266
8
6.9629
38
86.8619
8
.9876
38
22.2839
9
8.2600
39
89.9167
9
1.2500
39
23.4722
10
9.6296
40
940740
10
1.5432
40
246913
11
11.1018
41
98.3240
11
1.8673
41
26.9413
12
12.6666
^
102.6666
12
2.2222
42
27.2222
13
14.3240
43
107.1018
13
2.6080
43
28.5360
14
ia0740
44
111.6296
14
3.0247
44
29.8765
15
17.9167
45
116.2500
15
3.4722
46
31.2600
16
19.8519
46
120.9629
16
3.9606
46
32.6643
17
21.8796
47
125.7686
17
44599
47
340896
18
240000
48
130.6666
18
5.0000
48
36.5666
19
26.2120
49
135.6573
19
5.5710
49
37.0624
20
28.5185
50
140.7408
20
6.1728
50
38.6802
21
30.9166
51
145.9166
21
6.8066
51
40.1388
22
33.4073
82
161.1851
22
7.4691
62
41.7283
23
35.9906
53
156.5462
23
8.1636
53
43.3487
24
38.6666
54
im.(mo
24
8.8889
54
45.0000
26
^4352
55
167.5462
26
9.6466
56
46.6820
26
4420^
56
173.1851
26
10.4*21
66
48.3960
27
47.2500
67
178.9166
27
11.2500
57
60.1388
28
50.2962
58
184.7408
28
12.0687
68
61.9135
29
53.4352
59
190.6573
29
12.9782
59
63.7191
30
.:
5&6666
60
196.6666
30
13.8889
60
66.6665
"
( Ixxx. )
BASE 27— SLOPE 3 to 1.
>
i
a
1
Add.
}
Add.
R
1
Dedoct.
Dif.of
Hts.
Deduct.
.5655
31
68.8888
.0185
31
17.7963
2
1.2222
32
72.8888
2
.0740
32
18.9630
3
2.0000
33
77.0000
3
.1667
33
20.1666
4
2.8888
34
81.2222
4
.2963
34
21.4074
6
3.8888
35
86.5666
5
.4628
36
22.6851
6
5.0000
36
90.0000
6
.6667
36
24.0000
7
6.2222
37
94.5565
7
.9074
37
25.3618
8
7.5556
38
99.2222
8
1.1862
38
26.7407
9
9.0000
39
104.0000
9
1.5000
39
28.1666
10
10.6565
40
108.8888
10
1.8518
40
29.6296
11
12.2222
41
113.8888
11
2.2407
41
31.1296
12
14.0000
42
119.0000
12
2.6667
42
32.6666
13
16.8888
43
124.2222
13
3.1296
43
34.2407
14
17.8888
44
129.6566
14
3.6296
44
36.8518
15
20.0000
46
135.0000
15
4.1667
46
37.6000
16
22.2222
46
140.5665
16
4.7407
46
39.1851
17
24.5655
47
146.25^22
17
6.3618
47
40.9074
18
27.0000
48
152.0000
18
6.0000
48
42.6666
19
29.6556
49
157.8888
19
6.6862
49
44.4629
20
32.JK222
50
163.8888
20
7.4074
50
46.2963
21
35.0000
51
170.0000
21
8.1667
51
49.1666
22
37.8888
52
176.2222
22
8.9629
62
60.0740
■ 23
40.8888
53
1 82.5555
23
9.7962
53
52.0186
24
44.0000
54
189.0000
24
10.6667
54
64.0000
26
48.2222
55
196.5555
25
11.5741
66
56.0184
26
60.5556
56
202.2222
26
12.5184
56
58.0740
27
64.0000
67
209.0000
27
13.6000
57
60.1666
28
67.5556
68
215.8888
28
14.5185
58
62.2962
29
61.2222
59
222.8888
29
15.5741
59
64.4629
1
30
65.0000
60
230.0000
30
16.6667
60
66.6666
(Ixxxi. )
W|BA8E 28— SLOPE i to 1.
1
Add.
1
Add.
Deduct.
Deduct.
»
IS
1
O*
1
.5231
31
20.6231
.0015
81
1.4830
2
1.0555
32
21.3333
2
.0062
32
1.6802
3
1.5972
33
22.1627
8
.0189
33
1.6805
4
2.1481
34
22.9814
4
.0246
34
1.7839
5
2.7083
35
23.8194
5
.0386
35
1.8904
6
3.2777
36
24.6666
6
.0555
36
2.0000
7
3.8564
37
25.6231
7
.0756
37
2.1126
8
4.4444
38
26.3888
8
.0988
38
2.2284
9
5.0416
39
27.2639
9
.1250
39
2.8472
10
5.6481
40
28.1481
10
.1543
40
2.4691
11
6.2639
41
29.0416
11
.1867
41
2.5941
12
6.8888
42
29.9444
12
.2222
42
2.7222
13
7.5231
43
30.8564
13
.2608
43
2.8545
14
8.1666
44
31.7777
14
.3025
44
2.9876
15
8.8194
45
32.7083
16
.8472
45
3.1250
16
9.4814
46
33.6481
16
.3951
46
3.2654
17
10.1627
47
34.6972
17
.4460
47
8.4089
18
10.8333
48
35.5555
18
.6000
48
3.6555
19
11.6231
49
36.5231
19
.6571
49
3.7052
20
12.2222
50
37.5000
20
.6173
50
3.8580
21
12.9305
61
38.4861
21
.6806
51
4.0139
22
13.6481
52
39.4814
22
.7469
52
4.1728
23
143750
53
40.4861
23
.8163
53
4.3349
24
15.1111
64
41.5000
24
.8889
64
4.6000
25
15.8664
56
42.6231
26
•
.9647
65
46682
26
16.6111
66
43.6666
26
1.0432
66
48395
27
17.3760
57
44.5972
27
1.1250
57
5.0139
28
18.1481
58
46.6481
28
1.2099
68
6.1913
29
18.9305
69
46.7083
29
1.2978
69
5.8719
30
19.7222
60
47.7777
30
1.8889 60
H
5.5566
■
( Ixxxii. )
BASE 28— SLOPE ^ to 1.
5
S
O •
1
Add.
•r
31
Add.
Deduct.
gn
Deduct.
.6277
249722
1
.0031
31
2.9660
2
1.0740
32
26.0740
2
.0123
32
3.1606
3
1.6368
33
27.1944
3
.0278
33
3.3611
4
2.2222
34
28.3333
4
.0494
84
3.5679
6
2.8240
35
29.4907
6
.0772
35
3.7808
6
a4444
36
30.6666
6
.1111
86
4.0000
7
40833
37
31.8611
7
.1512
37
4.2263
8
47407
38
33.0740
8
.1976
38
4.4568
9
5.4166
39
343056
9
.2600
39
4.6944
10
anil
40
35.5555
10
•oOoD
40
49383
11
&8240
41
36.8240
11
.3734
41
5.1883
12
7.5655
^
38.1111
12
.4444
42
5.4444
13
8.3055
43
39.4166
13
.5216
43
6.7067
14
9.0740
44
40.7407
14
.6049
44
6.9763
15
9.8611
46
^.0633
15
.6944
45
&2500
16
10.6666
46
43.4444
16
.7901
46
6.5308
17
11.^06
47
44.8240
17
.8920
47
6.8179
18
12.3333
48
46i2222
18
1.0000
48
7.1111
19
13.1944
49
47.6889
19
1.11<^
49
7.4106
20
14.0740
50
49.0740
20
1.2346
50
7.7160
21
149722
51
50.62T7
21
1.3611
51
8.0277
22
16.8888
52
52.0000
22
1.4938
52
8.3466
23
1&8240
53
53.^07
23
1.6327
53
8.6697
24
17.7777
54
55.0000
24
1.7778
54
9.0000
25
18.7600
55
56.6277
25
1.9295
55
9.3364
26
19.7407
56
58.0740
26
2.0864
66
9.6790
27
20.7600
57
69.6389
27
2.2600
57
10.0277
28
21.7777
68
61.229ia
28
2.4197
58
10.3827
29
22.8240
69
^.8240
29
2.5956
59
10.7438
30
23.8888
60
64.4444
30
2.7778
60
11.1111
( Ixxziii. )
BASE 28 SLOPE f to 1.
1
a
Add.
1
s
31
Add.
1
Deduct.
Deduct.
1
.5323
29.4218
.0046
31
4.4490
2
L0925
32
30.8148
2
.0185
32
47407
8
1.6805
33
32.2861
8
.0416
33
5.0416 .
4
2.29^
84
33.6851
4
.0740
34
5.3518
6
2.9397
35
36.1620
5
.1157
36
66712
6
3.6111
36
36.6666
6
.1667
86
6.0000
7
4.3101
37
38.1990
7
.2268
37
6.8379
8
6.0370
38
39.7692
8
.2963
38
6.6851
9
6.7916
39
41.3470
9
.3750
89
7.0416
10
6.6740
40
42.9629
10
.4630
40
7.4074
11
7.8842
41
44.6064
11
.6602
41
7.7824
12
8.2222
42
46.2777
12
.6667
42
8.1666
13
9.0879
43
47.9768
13
.7824
48
8.5602
14
9.9815
44
49.7037
14
.9074
44
8.9629
15
10.9027
46
51.4583
15
1.0417
46
9.3760
16
11.8518
46
63.2407
16
1.18S2
46
9.7962
17
12.8286
47
55.0508
17
1.3379
47
10.2268
18
1^8333
48
56.8888
18
1.6000
48
10.6666
19
14.8657
49
58.7647
19
1.6713
49
11.1167
20
15.9258
60
60.6481
20
1.8618
50
11.5740
i 21
17.0138
51
62.6694
21
2.0417
51
12.0416
22
18.1296
52
64.6185
22
2.2407
62
12.6185
23
19.2731
53
66.4953
23
2.4491
53
13.0046
24
20.4444
54
68.6000
24
2.6667
54
13.6000
25
21.6435
65
70.6328
26
2.8935
55
14.0046
26
22.8703
56
72.6926
26
3.1296
56
14.6185
27
24.1250
67
74.6806
27
3.8750
57
15.0416
28
25.4074
68
76.7962
28
8.6296
58
15.5740
29
26.7176
69
78.9397
29
8.8936
59
16.1157
30
28.0556
60
81.1111
80 4.1667
60
16.6666
( Ixxxiv. )
BASE 28— SLOPE 1 to 1. 1
1
Add.
Add.
Dif.of
Hte.
Deduct.
Dif.of
Hit.
Deduct*
1
U5870
81
83.8704
I
.0062
31
5.9321
2
1.1111
82
35.6555
2
.0247
82
6.3210
3
1.7222
38
87.2777
8
.0555
38
6.7222
4
2.370S
84
39.0370
4
.0988
84
7.1358
6
3.0555
35
40.8333
5
.1543
85
7.5617
6
8.7777
86
42.6666
6
.2222
36
8.0000
7
4.5370
87
445370
7
.3025
37
8.4506
8
5.3333
88
46.4444
8
.3951
38
8.9135
9
6.1666
89
48.3888
9
.5000
89
9.3888
10
7.0370
40
50.3703
10
.6173
40
9.8765
n
7.9444
41
52.8888
11
.7469
41
10.3765
12
8.8888
4Si
54.4444
12
.8889
42
10.8888
13
9.8708
43
56.5370
13
1.0432
43
11.4135
14
10.8888
44
68.6666
14
1.2099
44
11.9506
15
11.9444
45
60.8333
16
1.3889
46
12.5000
16
13.0370
46
63.0370
16
1.6802
46
13.0617
17
14.1666
47
65.2777
17
1.7839
47
13.6358
18
15.3333
48
67.6566
18
2.0000
48
14.2222
19
16.6370
49
69.8704
19
2.2284
49
14.8209
20
17.7777
50
72.2222
20
2.4691
50
15.4321
21
19.0555
51
746111
21
2.7222
51
16.0555
22
20.3703
52
77.0370
22
2.9876
52
16.6913
23
21.7222
53
79.6000
23
3.2654
53
17.3395
24
23.1111
54
82.0000
24
3.5655
54
18.0000
25
24.5370
55
84,6370
25
3.8680
55
18.6728
26
26.0000
56
86.1111
26
41728
56
19.3580
27
27.6000
57
89.7222
27
46000
57
20.0555
28
29.0370
58
92.3703
28
48396
58
20.7654
29
30.6111
59
95.0666
29
6.1913
69
21.4876
30
32.2222 60
97.7777
30
5.5665
60
22.2222
(Ixxxv.)
BASE 28— SLOPE 1^ to 1.
1
Add.
1
Add.
Dif.or
Hts.
Deduct.
I>if.of
Htf.
Deduct.
1
.6416
81
38.3194
1
.0077
81
7.4151
2
1.1296
32
40.2962
2
.0309
32
7.9012
3
1.7638
33
42.3194
8
.0694
83
8.4027
4
2.4444
34
443888
4
.1234
34
8.9197
5
3.1712
36
46.6046
6
.1928
36
9.4621
6
8.9444
36
48.6666
6
.2778
36
10.0000
7
4.7638
87
60.8760
7
.3781
37
10.6632
8
6.6296
38
63.1296
8
.4938
38
11.1419
9
6.6416
39
66.4306
9
.6250
39
11.7361
10
7.6000
40
67.7777
10
.7716
40
12.3466
11
8i)046
41
60.1712
11
.9336
41
12.9706
12
9.6666
42
62.6111
12
1.1111
42
13.6111
13
10.6627
43
65.0972
13
1.3040
48
14.2680
14
11.7962
44
67.6296
14
1.6123
44
14.9382
16
12.9860
46
70.2088
16
1.7361
46
16.6250
16
14.^22
46
72.8333
16
1.9763
46
16.3271
17
16.6046
47
76.6046
17
2.2299
47
17.0447
18
16.8333
48
78.2222
18
2.5000
48
17.7777
19
18.2083
49
80.9860
19
2.7855
49
18.5262
20
19.6296
50
83.7962
20
3.0864
50
19.2901
21
21.0972
61
86.6627
21
3.4028
61
20.0694
22
22.6111
62
89.6656
22
3.7346
62
20.8641
23
24.1712
63
92.5046
23
4.0818
63
21.6748
24
26.7777
64
95.6000
24
44444
54
22.6000
26
27.4306
66
98.6416
26
48228
66
23.8410
26
29.1296
66
100.6296
26
6.2160
66
24.1976
27
30.8760
67
104.7638
27
6.6250
67
26.(J694
28
32.6666
68
107.9444
28
6.0494
68
26.9567
28
34.5046
69
111.1712
29
6.4891
69
26.8596
30 136.3888
60
1144444
30
&9444
60
27.7777
1
( Ixxzvi. )
BASE 28— SLOPE 1^ to 1.
Add.
1
Add.
1
Dednct.
Dedaet.
1
.5462
31
42.7686
.0092
81
8.8981
2
1.1481
32
45.0370
2
.0370
32
9.4815
3
1.8055
33
47.3611
3
.0833
83
10.0833
4
2.5185
34
49.7407
4
.1480
34
10.7087
5
3i2869
35
52.1759
5
.2813
35
11.3^125
6
4.1111
36
54.6666
6
.3388
86
12.0000
7
4.9906
37
57.2129
7
.4537
37
12.6769
8
5.9260
38
59.8148
8
.5926
38
13.3708
9
6.9166
89
62.4722
9
.7500
39
14.0833
10
7.9629
40
65.1851
10
.9259
40
14.8148
11
9.0648
41
67.9536
11
1.1203
41
15.5648
12
10.2222
^
70.7777
12
1.3383
42
16.3333
13
11.4351
43
73.6574
13
1.5648
48
17.1202 -
14
12.7037
44
76.6926
14
1.8148
44
17.9259
15
140277
45
79.5833
15
2.0833
46
18.7500
16
15.4074
46
82.6296
16
2.3704
46
19.5925
17
16.8426
47
ft5.7314
17
2.6759
47
20.4637
18
18.3333
48
88.8888
18
3.0000
48
21.8338
19
19.8796
49
92.1017
19
SM26
49
22.2314
20
21.4816
50
95.3703
20
3.7037
50
23.1481
21
23.1388
51
98.6944
21
4.0833
51
24.0838
22
24.8518
52
102.0740
22
4.4815
62
26.0370
23
26.6203
53
105.5092
23
4.8981
63
26.0092
24
28.4444
54
109.0000
24
5.3333
54
27.0000
25
30.3240
55
112.5462
25
5.7869
56
28.0092
26
32.2592
56
115.1481
26
6.2592
66
29.0370
27
34.2500
57
119.8055
27
a7500
57
80.0838
28
36.2962
58
123.5185
28
7.2592
68
31.1481
29
38.3981
59
127.2870
29
7.7869
59
82.2314
30
40.5555
60
131.1111
30
8.8333
60
33.3338
( Ixxxvii. )
BASE 28— SLOPE 1* to 1.
>M Height
Add.
Height
Add.
1
Deduct.
Dif. of
Uta.
Deduct.
.5508
31
47.2177
.0108
31
10.3811
2
1.1666
32
49.7777
2
.0432
^
11.0617
3
1.8472
33
62.4028
3
.0972
33
11.7638
4
2.5926
34
55.0926
4
.1728
34
12.4876
5
3.4027
85
67.8472
5
.2700
36
ia2330
6
4.2777
86
60.6666
6
.3889
36
140000
7
5.2177
37
63.6608
7
.5293
37
14.7885
8
6.2222
38
66.5000
8
.6913
38
15.6987
9
7.2916
39
69.5138
9
.8760
39
16.4305
10
8.4258
40
72.6926
10
1.0802
40
17.2839
11
9.6250
41
76.7360
11
1.3071
41
18.1689
12
10.8888
4&
78.9444
12
1.6656
4Si.
19.0566
13
12.2176
48
82.2176
13
1.8256
48
19.9747
14
laoiii
44
86.5665
14
2.1173
44
20.9185
15
15.0693
45
88.9683
16
2.4305
45
21.8760
16
16.5026
46
92.4259
16
2.7664
«
22.8580
17
18.1806
47
95.9683
17
3.1219
47
28.8626
18
19.8333
48
99.6556
18
a5ooo
48
248888
19
21.6609
^
108.2176
19
3.8997
49
25.9867
20
23.3333
60
106.9444
20
4.3210
50
27.0061
21
26.1806
51
110.7360
21
4.7639
51
28.0972
22
27.0926
52
1146926
22
6.2284
62
29.2098
23
29.0693
58
118.6188
23
5.7146
63
80.8441
24
31.1111
54
122.6000
24
6.2222
54
81.5000
25
38.2176
65
126.5606
25
6.7516
55
32.6774
26
36.3888
56
129.6666
26
7.3024
66
33.8765
27
37.6250
67
134.8472
27
7.8760
67
86.0972
28
39.9258
68
139.0926
28
8.4691
68
36.8894
29
^.2916
59
14a4028
29
9.0848
59
87.6038
30
4472221 60
147.7777
Iso
9.7222 \ 60
88.8888
( Ixxxviii. )
BASE 28— SLOPE 2 to 1.
J
n
Add.
t
31
Add.
gw
1
Dednct.
31
Dednct.
1
.5555
61.6666
.0123
11.8642
2
1.1861
32
54.6185
2
.0494
32
12.6419
3
1.8888
33
67.4444
3
.1111
33
13.4444
4
2.6666
34
60.4444
4
.1976
34
142716
5
3.5185
35
63.5185
6
.3086
35
16.1234
6
4.4444
36
66.6666
6
.4444
36
16.0000
7
5.4444
37
69.8888
7
.6049
37
16.9012
8
6.5185
38
73.1851
8
.7901
38
17.8271
9
7.6666
39
76.6656
9
1.0000
39
18.7777
10
8.8888
40
80.0000
10
1.2346
40
19.7530
11
10.1862
41
83.6185
11
l.'^38
41
20.7630
12
11.5565
42
87.1111
12
1.7778
42
21.7777
13
13.0000
43
90.7777
13
2.0664
43 B2.8271 |
14
14.5185
44
945186
14
2.4197
44
23.9012
15
16.1111
45
98.3333
15
2.7778
45
26.0000
16
17.7777
46
102.2222
16
3.1605
46
26.1234
17
19.5185
47
106.1861
17
3.5679
47
27.2716
18
21.3333
48
110.2222
18
40000
48
28.4444
19
23.2222
49
113.3333
19
44668
49
29.6420
20
26.1861
50
118.5185
20
49382
60
30.86^
21
27.2222
51
122.7777
21
6.4444
51
32.1111
22
29.3333
52
127.1111
22
6.9763
62
33.3827
23
31.5185
53
131.5186
23
6.6309
63
34.6790
24
33.7777
64
136.0000
24
7.1111
64
36.0000
25
3ftllll
55
140.6655
25
7.7160
56
37.3466
26
38.6185
56
144.1861
26
8.3467
66
38.7160
27
41.0000
67
149.8888
27
9.0000
67 '
iO.llll
28
43.5556
68
154.6666
28
9.6790
68 '
11.5308
29
46.1861
59
169.5186
29 :
10.3827
69 ^
12.9753
30
48.8888
60
1644444
30 :
11.1111 60 l(
14.4444
1
( Ixzxix. )
BASE 28 SLOPE 2J to 1.
1
Add.
1
Axld.
if. of
Bts.
Deduct.
3^
^33
1
Deduct. ,
K
K
1
Q
•
1
.5647
31
60.5647
.0164
31
14.8302 ;
2
1.2222
32
64.0000
2
.0617
32
15.8015
3
1.9722
33
67.K77
3
.1389
33
1^8055 :
4
2.8148
34
71.1481
4
.2468
34
17.8396
5
3.7500
35
74.8611
6
.3867
36
18.9043
6
4.7777
36
78.6666
6
.6665
36
20.0000
7
5.8980
37
82.5646
7
.7661
37
21.1265
8
7.1111
38
86.6665
8
.9876
38
22.2839 ■
9
8.4166
39
90.6389
9
1.2500
39
23.4722
10
9.8148
40
948148
10
1.6432
40
24.6913
11
11.3055
41
99.0833
11
1.8673
41
26.9413
12
12.8888
42
103.4444
12
2.22122
42
27.2222
13
14.5648
43
10?.8981
13
2.6080
43
28.5360
14
16.3333
44
112.4444
14
3.0247
44
29.8765 >
16
18.1944
45
117.0833
16
3.4722
45
31.2500
IB
20.1481
46
121.8148
16
3.9506
46
32.6543
17
22.1944
47
126.6389
17
4.4599
47
340895
18
24.3333
48
131.6555
18
5.0000
48
35.5555
19
26.5648
49
135.6646
19
6.6710
^
37.0624
20
28.8888
50
141.6666
20
6.1728
50
38.5802 :
21
dL3055
61
146.8611
21
&8055
61
40.1388 ■
22
33.8148
52
152.1481
22
7.4691
62
41.7283 '
23
36.4166
53
157.6277
23
8.1636
63
43.3487
24
39.1111
54
i6aoooo
24
8.8889
54
46.0000
25
41.8980
65
168.5647
25
9.6455
66
4a6820
26
44.7777
66
173.2222
26
10.4321
56
48.3950
27
47.7500
57
179.9722
27
11.2500
67
6ai388 i
28
50.8148
58
185.8148
28
12.0687
58
61.9136
29
53.9722
69
191.7500
29
12.9782
59
53.7191 '
30
67-2222
60
197.7777
30
13.8889
60
66.5565 1
(xc.)
BASE 28— SLOPE 3 to 1.
1
1
Add.
4^
1
Add.
3^
Dedact.
Deduct.
.5740
31
69.4630
1
.0185
31
17.7963
2
1.2592
32
73.4815
2
.0740
32
18.9630
3
2.0555
33
77.6111
3
.1667
33
20.1666
4
2.9630
34
81.8518
4
.2963
34
21.4074
5
3.9815
35
86.2037
6
.4628
36
22.6851
6
6.1111
36
90.6666
6
.6887
36
240000
7
6.3518
37
95.2404
7
.9074
37
25.3518
8
7.7037
38
99.9269
8
1.1852
38
26.7407
9
9.1666
39
1047222
9
1.5000
39
28.1666
10
10.7407
40
109.6296
10
1.8518
40
29.8296
11
12.4260
41
114.6481
11
2.2407
41
31.1296
12
14.222?,
42
119.7777
12
2.6667
42
32.8866
13
1&1296
43
126.0186
13
3.1296
43
342407
14
18.1481
44
130.3703
14
3.6296
44
35.8518
15
20.2777
45
135.8333
16
41667
46
37.6000
16
22.5185
46
141.4074
16
47407
46
39.1861
17
24.8708
47
147.0926
17
5.3518
47
40.9078
18
27.3333
48
152.8888
18
6.0000
48
42.6668
19
29.9074
49
167.7962
19
6.6862
49
444^29
20
32.5926
50
164.8148
20
7.4074
60
46.2963
21
35.3888
61
170.9444
21
8.1687
51
49.1666
22
38.2962
52
177.1861
22
8.9629
52
60.0740
23
41.3148
53
183.6370
23
9.7962
63
52.0185
24
44.4444
54
190.0000
24
10.6667
64
540000
25
4X6850
66
196.5470
25
11.6741
66
66.0184
26
61.0370
56
202.2592
26
12.5184
66
58.0740
27
54.5000
67
210.0556
27
13.5000
67
60.1666
28
58.0740
68
216.9630
28
146186
68
62.2962
29
61.7592
69
222.9814
29
16.6741
69
644639
30
65.5655
60
231.1111
30
16.6667
60
66.6666
(• xci. )
BASE 29-SLOPE i to 1.
•8
Add.
•8
Add.
Dednct.
3^
Deduct.
a
K
a
Q
1
.5416
31
21.0972
1
.0015
31
1.4830
2
1.0926
32
21.9259
2
.00^
32
1.5802
8
1.6527
33
22.7639
3
.0139
33
1.6805
4
2.2222
34
23.6111
4
.0246
34
1.7839
5
2.8009
85
24.4676
5
.0385
35
1.8904
6
3.3888
36
26.3333
6
.0555
36
2.0000
7
3.9861
37
26.2083
7
.0766
37
2.1126
8
4.5926
38
.27.0926
8
.0988
38
2.2284
9
5.2063
39
.27.9861
9
.1260
39
2.3472
10
5.8333
40
28.8888
10
.1543
40
2.4691
11
&4676
41
29.8009
11
.1867
41
2.6941
12
7.1111
^
30.7222
12
.2222
42
2.7222
13
7.7639
43
31.6527
13
.2608
43
2.8545
14
8.4259
44
32.6926
14
.3026
44
2.9876
15
9.0972
45
33.5416
15
.3472
45
ai250
16
9.7777
46
345000
16
.3961
46
3.2654
17
10.4676
47
35.4676
17
.4460
47
3.4089
18
11.1666
48
36.4444
18
.5000
48
3.5565
10
11.8760
49
37.4305
19
.5671
49
3.7052
20
12.5926
50
38.4259
20
.6173
60
3.8580
21
13.3194
51
39.4305
21
.6806
51
40139
22
14.0555
52
40.4444
22
.7460
62
41728
23
148009
53
41.4676
23
.8163
53
43349
24
15.5555
54
42JX)00
24
.8889
54
46000
25
16.3194
55
43.5416
26
.9647
55
46682
26
17.0926
56
44.6926
26
1.0432
56
48395
27
17.8760
57
45.6527
27
1.1260
67
5.0139
28
18.6666
58
46.7222
28
1.2099
68
5.1913
29
19.4676
69
47.8009
29
1.2978
59
5.3719
80
aO.2777
60
48.8888
30
1.3889
60
6.6555
1
( xdL )
BASE 29— SLOPE
r
; i to 1.
height
Add.
1
▲dd.
Deduct.
Deduct.
1
K
1
o
31
.54^2
31
26.6463
.0031
2.9660
2
1.1111
32
26.6666
2
.0123
82
3.3611
8
1.6944
33
27.8055
8
.0278
33
a6111
4
2.2962
34
28.9629
4
.0^4
84
3.6679
5
2.9166
35
30.1388
5
.0772
86
3.7808
6
3.5555
36
31.3333
6
.1111
86
40000
7
42129
37
32.6463
7
.1612
37
42258
8
48888
88
33.7777
8
.1975
38
4.4668
9
5.5833
39
36.0277
9
.2600
39
46944
10
6.2962
40
36.2962
10
.3086
40
49383
11
7.0278
41
37.5833
11
.8784
41
6.1883
12
7.7777
42
38.8888
12
.4444
42
5.4444
13
8.5463
43
40.2129
18
.5216
48
6.7076
14
9.3333
44
41.6566
14
.6049
44
5.9753
16
10.1388
45
42.9166
16
.6944
45
&2500
16
10.9629
46
4429^
16
.7901
46
&5308
17
11.8055
47
45.6944
17
.8920
47
6.8179
18
12.6666
48
47.1111
18
1.0000
48
7.1111
19
18.5463
49
^.6462
19
1.1142
49
7.4105
20
144444
60
50.0000
20
1.2346
50
7.7160
21
15.8611
61
51.4722
21
1.3611
51
8.02T7
22
16.2962
62
62.9629
22
1.4938
52
8.3466
23
17.2600
53
64.4722
23
1.6327
58
8.6607
24
18.2222
64
6aoooo
24
1.7778
54
9.0000
25
19.2129
56
57.546@
26
1.9295
65
9.3364
26
20.2222
66
69.1111
26
2.0864
56
9.6790
27
21.2500
57
60.6944
27
2.2500
57
10.0277
28
22.2962
58
62.2962
28
2.4197
58
10.3827
: 29
23.3611
59
63.9166
29
2.5966
59
10.7488
! 30
1
24.4444
60
66.5565
30
2,7778
60 11.1111
( xciii. )
BASE 29 SLOPE i to 1.
•s
X
1
Add.
1
Add.
Dif.of
Hts.
Deduct.
Dif.of
Hta.
Deduct.
.5508
31
29.9964
1
.0046
31
4.4490
2
1.1296
32
31.4074
2
.0186
32
4.7407
3
1.7361
33
32.8472
3
.0416
33
5.0416
4
2.3703
34
343147
4
.0740
34
5.3518
5
3.0323
35
35.8101
6
.1167
35
5.6712
6
3.7222
36
37.3333
6
.1667
36
6.0000
7
4.4397
37
38.8842
7
.2268
37
6.3379
8
6.1851
38
40.4629
8
.2963
38
6.6851
9
6.9583
39
42.0696
9
.3750
39
7.0416
10
6.7592
40
43.7037
10
' .4630
40
7.4074
11
7.5880
41
46.3657
11
.6602
41
7.7824
12
8.4444
42
47.0555
12
.6667
42
8.1666
13
9.3287
43
48.7731
13
.7824
43
8.5612
14
10.2407
44
50.5185
14
.9074
44
8.9629
15
11.1806
45
52.2916
15
1.0417
45
9.3750
16
12.1481
46
54.0926
16
1.1852
46
9.79^
17
13.1434
47
56.9212
17
1.3379
47
10.2268
18
14.1666
48
67.7777
18
1.5000
48
10.6660
19
15.2176
^
59.6620
19
1.6713
49
11.1167
20
16.2962
50
61.6740
20
1.8618
50
11.5740
21
17.4027
61
63.5140
21
2.0417
51
12.0416
22
18.5370
52
66.4814
22
2.2407
62
12.5185
23
19.6991
53
67.4768
23
2.4491
53
13.0046
24
20.8888
64
69.5000
24
2.6667
64
13.5000
25
22.1064
65
71.6608
26
2.8935
56
14.0046
26
23.3518
56
73.6296
26
3.1296
56
14.5185
27 24.6250
67
76.7361
27
3.3750
57
15.0416
28
25.9258
58
77.8703
28
3.6296
58
15.67^
29 27.2546
69
80.0323
29
3.8986
5e
16.1157
30 28.6111
60
82.2222
30
4.1667
60
16.6666
( xciv. )
BASE 29— SLOPE 1 to 1.
1
Add.
}
Add.
Deduct.
ftsSJ
Deduct.
to
B
a
Q
1
.5555
31
34.4444
1
.0062
31
6.9321
2
1.1481
32
36.1481
2
.0247
32
&3210
3
1.7777
33
37.8888
3
.0556
33
6.7222
4
2.4444
34
39.6666
4
.0988
34
7.1358
5
ai481
35
41.4814
5
.1643
35
7.5617
6
a8888
36
43.3333
6
.2222
36
8.0000
7
46666
37
45.2222
7
.3025
37
8.4506
8
5.4814
38
47.1481
8
.3951
38
8.9135
9
6.3333
39
49.1111
9
.5000
39
9.3888
10
7.2222
40
61.1111
10
.6178
40
9.8765
11
ai481
41
53.1481
11
.7469
41
10.3765
12
9.1111
42
55.2222
12
.8889
^
10.8888
13
10.1111
43
67.3333
13
1.0432
43
11.4135
14
11.1481
44
69.4814
14
1.2099
44
11.9506
15
12.2222
45
61.6666
16
1.3889
46
12.6000
16
13.3333
46
64.8888
16
1.5802
46
13.0617
17
14.4814
47
66.1481
17
1.7839
47
ia6358
18
15.6666
48
68.4444
18
2.0000
48
14.2222
19
16.8888
49
70.7777
19
2.2284
49
14.8209
20
18.1481
50
73.1481
20
2.4691
60
15.4321
21
19.4444
51
76.5555
21
2.7222
51
16.0565
22
20.7777
62
78.0000
22
2.9876
52
16.6913
23
22.1481
53
80.4814
23
a2664
63
17.3395
24
23.5555
54
82.0000
24
3.5566
64
18.0000
26
25.0000
55
85.5665
26
a8630
55
ia6728
26
26.4815
56
88.1481
26
4.1728
56
19.3580
27
28.0000
67
90.7777
27
4.5000
57
20.0555
28
29.5555
68
93.4444
28
4.8395
58
20.7654
29
31.1481
59
96.1481
29
5.1913
69
21.4876
30
32.7777
60
98.8888
30
5.6655
60
( «T. )
BASE 29— SLOPE li to 1.
1
•8
Add.
*
Add.
if. of
Deduct.
if. of
Hti.
Deduct.
X
1
31
Q
Q
.5601
38.8935
1
.0077
31
7.4161
2
1.1666
32
40.8888
2
.0309
32
7.9012
3
1.8194
33
^.9305
3
.0694
33
8.4027
4
2.6185
34
45.0185
4
.1234
34
8.9197
5
3.2638
35
47.1527
5
.1928
35
9.4621
6
4.0555
36
49.3333
6
.2778
36
10.0000
7
4.8934
37
51.6601
7
.3781
37
10.5632
8
5.7777
38
63.8333
8
.4938
38
11.1419
9
6.7083
39
66.1527
9
.6250
39
11.7361
10
7.6851
40
58.5185
10
.7716
40
12.3456
11
8.7083
41
60.9305
11
.9336
41
12.9706
12
9.7777
42
63.3888
12
1.1111
^
13.6111
13
10.8934
43
66.8936
13
1.3040
43
14268G
14
12.0555
44
68.4444
14
1.5123
44
149382
15
13.2638
45
71.0416
15
1.7361
45
15.6250
16
14.5185
46
74.6851
16
1.9753
46
16.3271
17
15.8194
47
76.3750
17
2.2299
47
17.0447
18
17.1666
48
79.1111
18
2.5000
48
17.7777
19
18.5601
49
81.8935
19
2.7855
49
18.5262
20
20.0000
50
84.7222
20
3.0864
50
19.2901
21
21.4861
61
87.5972
21
3.4028
61
20.0694
22
23.0185
52
90.5186
22
3.7346
52
20.8641
23
245972
63
93.4860
23
4.0818
53
21.6743
24
26.2222
54
95.5000
24
4.4444
54
22.6000
25
27.8935
55
99.5601
25
4.8228
56
23.3410
26
29.6111
56
102.6666
26
6.2160
66
24.1975
27
31.3750
57
106.8194
27
5.6260
57
25.0694
28
33.1851
68
109.0186
28
6.0494
58
25.9667
29
35.0416
59
112.2638
29
6.4891
59
26.8595
80
36.9444
60
116.5555
30
6.9444
60
27.7777
( xcvi. )
BASE 29— SLOPE IJ to 1.
1
Add.
1
Add.
^9
Dednct.
SIS
Deduct.
V
s
Q
Q
1
.6647
31
43.3426
1
.0092
31
8.8981
2
1.1851
32
46.6296
2
.0370
32
9.4816
3
1.8611
33
47.9722
3
.0833
33
10.0833
4
2.5926
34
50.3703
4
.1480
34
10.7037
5
3.3796
35
62.8240
6
.2313
35
11.3426
6
42222
36
66.3333
6
.3333
36
12.0000
7
6.1202
37
67.8980
7
.4537
37
12.6769
8
6.0740
38
60.5186
8
.5926
38
13.3703
9
7.0833
39
63.1944
9
.7500
39
140833
10
8.1481
40
66.9269
10
.9259
40
148148
11
9.2685
41
08.7129
11
1.1203
41
16.6648
12
10.4444
42
71.6655
12
1.3333
42
ia3333
13
11.6758
43
74.4537
13
1.5648
43
17.1202
14
12.9629
44
77.4074
14
1.8148
44
17.9269
15
14.3065
46
80.4166
15
2.0833
46
18.7500
16
15.7037
46
84.4814
16
2.3704
46
19.6925
17
17.1573
47
86.6018
17
2.6750
47
20.4637
18
18.6666
48
89.7777
18
3.0000
48
21.3333
19
20.2314
49
93.0092
19
3.3426
49
22.2314
20
21.8618
60
96.29^
20
3.7037
50
23.1481
21
23.5277
61
99.6388
21
4.0833
51
24.0833
22
26.2592
62
103.0370
22
44815
52
25.0370
23
27.0462
63
106.4906
23
48981
53
26.0092
24
28.8888
64
109.0000
24
5.3333
64
27.0000
26
30.7870
55
113.6647
25
6.7869
56
28.0092
26
32.7407
66
117.1852
26
6.2592
66
29.0370
27
34.7500
67
120.8611
27
6.7600
57
30.0833
28
36.8147
68
124.6926
28
7.2592
58
31.1481
29
38.9361
69
128.3796
29
7.7869
59
32.2314
30
41.1111
60
132.2222
30 8.33331
60
3a3333
( xcvii. )
BASE 29— SLOPE If to 1.
Height
Add.
■s
»
Add.
1
Deduct.
Dif. of
Hts.
Deduct.
1
.6692
31
47.7917
.0108
31
10.3811
2
1.2037
32
50.3708
2
.0482
82
11.0617
3
1.9028
33
63.0140
3
.0972
38
11.7638
4
2.6666
84
65.7222
4
.1728
84
12.4876
5
3.4952
36
58.4968
6
.2700
85
18.2830
6
4.3888
36
61.3383
6
.8889
86
14.0000
7
5.3470
37
64.2360
7
.6293
37
14.7885
8
6.37^
88
67.2087
8
.6913
38
15.5987
9
7.4583
39
70.2360
9
.8760
89
16.4305
10
8.6111
40
78.8388
10
1.0802
40
17.2839
11
9.8286
41
76.4958
11
1.3071
41
18.1689
12
11.1111
42
79.7222
12
1.6666
42
19.0555
13
12.4582
43
88.0140
18
1.8256
43
19.9747
14
13.8708
44
86.8703
14
2.1173
44
20.9185
15
16.8470
46
89.7917
15
2.4305
45
21.8750
16
1&8888
46
94.2777
16
2.7654
46
22.8580
17
18.4962
47
96.8286
17
3.1219
47
28.8626
18
20.1666
48
100.4444
18
8.5000
48
24.8888
19
21.9027
49
104.1250
19
8.8997
49
26.9867
20
23.7037
60
107.8708
20
4.8210
50
27.0061
21
25.6694
51
111.6805
21
4.7639
51
28.0972
22
27.6000
52
115.5655
22
5.2284
52
29.2098
23
29.4952
53
119.4962
23
5.7146
63
30.8441
24
31.5566
64
122.6000
24
6.2222
54
31.6000
25
33.6806
65
127.5694
25
6.7516
65
32.6774
26
86.8703
66
131.7037
26
7.8024
66
83.8765
27
38.1260
57
ia5.9027
27
7.8750
67
36.0972
28
40.4444
58
140.1666
28
8.4691
58
86.8394
29
42.8286
69
144.4962
29
9.0848
69
37.6033
80
46.2777
60
148.8888
30
9.7222
60
38.8888
1
I
( xcviii. )
BASE 29-SLOPE 2 to 1.
t
Add.
•s
Add.
Si as
Deduct.
5S3
Deduct.
»
cs
1
Q
1
.6740
31
62.2407
.0123
31
11.8642
2
1.2222
32
55.1111
2
.0494
32
12.6419
3
1.9444
33
68.0566
3
.1111
33
13.4444
4
2.7407
34
61.0740
4
.1975
34
14.2716
5
3.6111
36
64.1666
6
.3086
36
16.1234
6
4.6555
36
67.3333
6
.4444
36
16.0000
7
5.5740
37
70.6740
7
.6049
87
16.9012
8
6.6666
38
73.8888
8
.7901
38
17.8271
9
7.8333
39
77.2777
9
1.0000
89
18.7777
10
9.0740
40
80.7407
10
1.2346
40
19.7530
11
10.3888
41
842777
11
1.4938
41
20.7630
12
11.7777
42
87.8888
12
1.7778
42
21.7777
13
13.1406
43
91.5740
13
2.0864
43
22.8271
14
14.7777
44
95.3333
14
2.4197
44
23.9012
•
15
16.3888
45
99.1666
15
2.7778
46
25.0000
16
18.0740
46
104.0740
16
3.1606
46
26.1234
17
19.8333
47
107.0555
17
3.6679
47
27.2716
18
21.6666
48
iii.iin
18
4.0000
48
28.4444
19
23.5740
49
115.2407
19
4.4568
49
29.6^20
20
25.5555
50
119.4444
20
4.9382
60
80.8642
21
27.6111
61
123.7222
21
5.4444
51
32.1111
22
29.7407
52
128.0740
22
5.9753
62
33.3827
23
31.9444
53
182.6000
23
6.6809
53
34.6790
24
34.2222
54
136.0000
24
7.1111
54
36.0000
25
36.6740
65
141.6740
25
7.7160
66
37.8466
26
39.0000
56
146.2222
26
8.3457
56
88.7160
27
41.5000
67
160.9444
27
9.0000
57
40.1111
28
44.0740
58
166.7407
28
9.6790
68
41.5808
29
46.7222
59
160.6111
29
10.3827
69
42.9763
30
49.4444
60
165.5556
80
11.1111
60
44.4444
( xctx. )
BASE 29 SLOPE
2| to 1.
m
1
Add.
1
»
Add.
Deduct.
Deduct.
.5833
31
61.1388
1
.0164
31
14.8302
2
1.2592
32
64.6926
2
.0617
32
16.8013
8
2.0277
33
68.1389
3
.1389
S3
ia8055
4
2.8888
34
71.7777
4
.2468
34
17.8395
5
3.8426
35
76.5092
5
.3867
36
18.9043
6
4.8888
36
79.3333
6
.5665
36
20.0000
7
6.0277
37
83.2600
7
.7561
37
21.1265
8
7.2592
38
87.2592
8
.9876
38
22.2839
9
8.5833
39
91.3611
9
1.2500
39
23.4722
10
10.0000
40
96.6665
10
1.5432
40
246913
H
11.5092
41
99.8426
11
1.8673
41
25.9413
12
13.1111
42
104.2222
12
2.2222
42
27.2222
13
14.8054
43
108.6944
13
2.6080
43
28.5360
14
16.5926
44
113.2592
14
3.0247
44
29.8765
16
18.4722
45
117.9166
16
3.4722
46
31.2600
16
20.4444
46
123.6666
16
3.9506
46
32.6543
17
22.5092
47
127.5092
17
4.4599
47
340896
18
24.6666
48
132.4444
18
5.0000
48
36.6655
19
26.9166
49
137.4722
19
6.5710
49
37.0524
20
29.2592
50
142.6926
20
6.1728
50
3a6802
21
31.6944
51
147.8066
21
6.8056
51
40.1388
22
34.2222
52
153.1111
22
7.4691
52
41.7283
23
36.8426
53
158.5092
23
8.1636
53
43.3487
24
39.5555
54
163.0000
24
8.8889
54
45.0000
25
42.3610
55
169.5833
25
9.6466
55
46.6820
26
45.2592
56
175.2592
26
10.4321
56
48.3950
27
48.2500
57
181.0277
27
11.2500
67
60.1388
28
51.3333
68
186.8888
28
12.0687
68
51.9135
29
54.5092
59
192.8425
29
12.9782
69
53.7191
30
57.7777
60
198.8888
30
13.8889
60
65.6656
(c)
BASE 29— SLOPE 3 to 1.
•4*
1
1
Add.
1
Add.
3^
1
Deduct.
I>if.of
Ht8.
Deduct.
.&926
31
70.0370
.0185
31
17.796a
2
1.2962
32
740740
2
.0740
32
18.9630
a
2.1111
33
78.2222
3
.1667
33
20.1666
4
3.0370
34
82.4814
4
.2963
34
21.4074
6
40740
35
86.8618
5
.4628
35
22.6851
6
5.2222
36
91.3333
6
.6667
36
240000
7
6.4813
37
96.9268
7
.9074
37
25.3518
8
7.8618
38
100.6296
8
1.1862
38
26.7407
9
9.3333
39
106.4444
9
1.6000
39
28.1666
10
10.9259
40
110.3703
10
1.8618
40
29.6296
11
12.6296
41
116.4074
11
2.2407
41
31.1296
12
14.4444
42
120.5555
12
2.6667
42
32.6666
13
16.3703
43
126.8148
13
3.1296
43
34.2407
14
18.4074
44
131.1861
14
3.6296
44
35.8518
15
20.5555
45
136.6666
15
41667
45
37.5000
16
22.8148
46
143.2692
16
47407
46
39.1861
17
25.1851
47
147.9628
17
6.3618
47
40.9074
18
27.6666
48
163.7777
18
6.0000
48
42.6666
19
30.2592
49
169.7037
19
6.6862
49
44.4629
20
32.9629
50
165.7407
20
7.4074
60
46.2963
21
36.7777
51
171.8888
21
8.1667
51
49.1666
22
38.7037
62
178.1481
22
8.9629
62
50.0740
23
41.7407
63
1845186
23
9.7962
53
52.0185
24
44.8888
54
190.0000
24
10.6667
54
54.0000
25
48.1480
65
197.5926
25
11.6741
65
56.0184
26
61.5184
56
2042962
26
12.5184
56
58.0740
27
55.0000
67
211,1111
27
13,5000
57
60.1666
28
68.5926
58
218.0370
28
145186
68
62.2962
29
62.2962
59
226.0740
29
15.5741
69
64.4629
30
66.1111
60
232.2222
30
16.6667
60
66.6666
(oi.)
BASE 30— SLOPE i to 1.
V
Add.
1
Add.
Deduct.
Deduct.
»
X
1
31
1
.6602
31
21.6713
.0015
1.4830
2
1.1296
32
22.5186
2
.0062
32
1.5802
3
1.7083
33
23.3750
3
.0139
33
1.6805
4
2.2962
34
24.2407
4
.0246
34
1.7839
5
2.8935
35
25.1157
5
.0385
35
1.8904
6
3.6000
36
26.0000
6
.0565
36
2.0000
7
4.1157
37
26.8935
7
.0766
37
2.1126
8
4.7407
38
27.7963
8
.0988
38
2.2284
9
5.3750
39
28.7083
9
.1250
39
2.3472
10
6.0185
40
29.6296
10
.1543
40
2.4691
11
6.6713
41
30.5602
11
.1867
41
2.5941
12
7.3333
42
31.6000
12
.2222
42
2.7222
13
8.0046
43
32.4490
13
.2608
43
2.8545
14
8.6851
44
33.4073
14
.30-25
44
2.9876
15
9.3760
45
34.3750
15
.3472
45
3.1250
16
10.0740
46
35.3518
16
.3961
46
a2654
17
10.7824
47
36.3379
17
.4460
47
3.4089
18
11.5000
48
37.3333
18
.6000
48
3.5555
19
12.^268
49
38.3379
19
.5.571
49
3.7052
20
12.9629
60
39.3518
20
.6173
60
3.8580
21
13.7083
61
40.3750
21
.6805
51
4.0139
22
14.4629
62
41.4073
22
.7469
52
4.1728
23
15.2268
63
42.4490
23
.8163
53
4.3349
24
16.0000
54
43.5000
24
.8889
54
4.5000
25
16.7824
65
44.5602
25
.9647
55
4.6682
26
17.5740
56
46.6296
26
1.0432
66
4.8395
27
18.3760
67
46.7083
27
1.1250
67
5.0139
28
19.1851
58
47.7963
28
1.2099
58
5.1913
29
20.0046
59
48.8935
29
1.2978
59
5.3719
30
20.8333
60
60.0000
30
1.3889
60
5.5555
( cii. )
BASE 30— SLOPE i to 1.
•a
•8
Add.
1
Add.
Saru
Deduct.
Deduct.
1
31
1
a^
.6648
26.1203
.0031
31
2.9660
2
1.1481
32
27.2592
2
.0123
32
3.1605
3
1.7600
33
28.4166
3
.0278
33
33611
4
2.3704
34
29.6926
4
.0494
34
3.6679
3
3.0092
36
30.7870
5
.0772
36
3.7808
6
3.6666
36
32.0000
6
.1111
36
4.0000
7
4.3426
37
33.2316
7
.1612
37
4.2263
8
6.0370
38
34.4816
8
.1975
38
4.4668
9
6.7600
39
36.7600
9
.2600
39
4.6944
10
6.4816
40
37.0370
10
.3086
40
4.9383
11
7.23J6
41
38.3425
11
.3734
41
6.1883
12
8.0000
42
39.6666
12
.4444
42
5.4444
13
8.7870
43
41.0092
13
.6216
43
6.7067
14
9.6926
44
42.3704
14
.6049
44
5.9753
16
10.4166
46
43.7500
15
.6944
46
6.2600
16
11.2692
46
46.1481
16
.7901
46
6.6308
17
12.1203
47
46.6648
17
.8920
47
6.8179
18
13.0000
48
48.0000
18
1.0000
48
7.1111
19
13.8981
49
49.4637
19
1.11^
49
7.4106
20
14.8147
60
60.9260
20
1.2346
60
7.7160
21
16.7600
61
52.4166
21
1.3611
61
8.0277
•
22
16.7037
62
63,9260
56.4637
22
1.4938
62
8.3466
23
17.6759
63
23
1.6327
63
8.6697
24
18.6666
64
67.0000
24
1.7778
54
9.0000
26
19.6769
65
58.5648
26
1.9296
65
9.3364
26
20.7037
66
60.1481
26
2.0864
56
9.6790
27
21.7500
57
61.7600
27
2.26()0
67
10.0277
28
22.8147
68
63.3704
28
2.4197
68
10.3827
29
23.8981
69
65.0092
29
2.6956
69
10.7438
1
•
30i26.0000
60
66.6666
30
2.7778
60
11.1111
( ciiL )
BASE 30— SLOPE | to 1.
-a,
•s
Add.
1
2
3
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
26
26
27
28
29
30
•s
.5694
1.1666
1.7917
2.4444
3.1250
3.8333
4.5692
5.3333
6.1250
6.9444
7.7917
8.6666
9.5694
10.5000
1L4583
12.4444
13.4583
14.5000
15.5694
16.6666
17.7917
18.9444
20.1250
21.3333
22.5692
23.8333
25.1250
26.4444
27.7917
29.1666
Add.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
61
52
63
54
56
66
67
68
69
60
30.5694
32.0000
33.4683
34.9444
36.4583
38.0000
39.6694
41.1666
42.7917
44.4444
46.1250
47.8333
49.6692
51.3333
63.1250
64.9444
66.7917
58.6666
60.5694
62.5000
64.4683
66.4444
68.4583
70.5000
72.6694
74.6666
76.7917
78.9444
81.1250
83.3333
o •
Deduct.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
16
16
17
18
19
20
21
22
23
24
26
26
27
28
29
30
i
s
.0046
.0185
.0416
.0740
.1167
.1667
.2268
.2963
.3760
.4630
.5602
.6667
.7824
.9074
1.0417
1.1852
1.3379
1.5000
1.6713
1.8518
2.0417
2.2407
2.4491
2.6667
2.8935
3.1296
3.3750
3.6296
3.8936
4.1667
31
32
33
34
35
36
37
38
39
40
41
42
43
44
46
46
47
48
49
50
51
62
63
54
55
56
51
68
59
60
Deduct.
4.4490
4.7407
5.0416
6.3618
66712
6.0000
6.3379
6.6851
7.0416
7.4074
7.7824
8.1666
8.5602
8.9629
9.3750
9.7962
10.2268
10.6666
11.1157
11.5740
12.0416
12.5185
13.0046
13.5000
14.0046
14.6186
15.0416
15.6740
16.1157
16.6666
( «T. )
BASE 30— SLOPE 1 to 1.
•8
Add.
to
■s
Add.
Deduct.
Dedoct.
S
w
1
Q
1
.5740
31
35.0186
.0062
31
5.9321
2
1.1861
32
36.7407
2
.0247
32
6.321U
3
1.8333
33
88.5000
3
.05.55
33
6.7222
•
4
2.6186
34
40.2962
4
.0988
34
7.1358
5
3.2407
36
42.1296
5
.1643
36
7.6617
6
4.0000
36
44.0000
6
.2222
36
8.0000
7
4.7962
37
46.9074
7
.3025
37
8.4606
8
6.6296
38
47.8518
8
.3951
38
8.9136
9
6.5000
39
49.8333
9
.6000
39
9.3888
10
7.4074
40
51.8618
10
.6173
40
9.8766
11
8.3618
41
53.9074
11
.7469
41
10.3765
12
9.3333
42
66.0000
12
.8889
42
10.8888
13
10.3618
43
68.1296
13
1.0432
43
11.4135
14
11.4074
44
60.2962
14
1.2099
44
11.9506
15
12.6000
45
62.6000
15
1.3889
46
12.6000
16
13.^96
46
64.7407
16
1.6802
46
13.0617
17
14.7962
47
67.0186
17
1.7839
47
13.6358
18
16.0000
48
69.3333
18
2.0000
48
14.2222
19
17.2407
49
71.6851
19
2.2284
49
14.8209
20
18.5186
60
74.0740
20
2.4691
60
15.4321
21
19.8.333
61
76.6000
21
2.7222
51
16.0555
1
22
21.1851
52
78.9629
22
2.9876
62
16.6913
23
22.6740
53
81.4629
23
3.2654
63
17.3396
24
24.0000
54
84.0000
24
3.6656
54
18.0000
26
26.4629
66
86.6740
25
3.8580
55
18.6728
26
26.9629
66
89.1851
26
4.1728
66
19.3680
27
28.6000
57
91.8333
27
4.5000
57
20.0666
28
30.0740
68
94..5185
28
4.8396
58
20.7654
1
29
31.6861
59
97.2407
29
6.1913
69
21.4876
30
33.3333
60
100.0000 1 30
5.5665 60
22.2222
( cv. )
BASE 30— SLOPE IJ to 1.
S
S
0.5I
"8 J
X
AM.
Add.
. .3
Dedoek
2-«
Dedoot.
1
.6786
31
39.4676
.0077
31
7.4151
2
1.2037
32
41.4815
2
.0809
32
7.9012
3
1.8750
33
43.5417
8
.0694
38
8.4027
4
2.5926
34
45.6481
4
.1234
34
8.9197
5
3.3564
36
47.8009
6
.1928
35
9.4521
6
4.1666
36
50.0000
6
.2778
36
10.0000
7
5.0230
37
52.2453
7
.3781
37
10.6632
6
5.9259
38
64.5370
8
.4938
38
11.1419
9
6.8750
39
56.8760
9
-6260
39
11.7361
10
7.8703
40
69.2992
10
.7716
40
12.3466
11
8.9120
41
61.6898
11
.9336
41
12.9706
12
10.0000
42
64.1666
12
1.1111
42
laoiii
13
11.1344
43
66.6898
13
1.3040
43
14.2680
14
12.3148
44
69.2592
14
1.5123
44
14.9382
15
13.5416
45
71.8760
15
1.7361
46
15.6250
}6
14.8148
46
74.5370
16
1.9753
46
16.3271
17
16.1344
47
77.2463
17
2.2299
47
17.0447
IS
17.5000
48
80.0000
18
2.6000
48
17.7777
19
19.9120
49
^.8009
19
2.7855
49
18.5262
«)
20.3703
50
85.6481
20
3.0864
50
19.2901
21
21.8750
51
8a6417
21
3.4028
51
20.0694
i»
23.^59
52
91.4816
22
3.7346
52
20.8641
23
26.0230
53
94.4676
23
4.0818
53
21.6743
24
26.6666
54
97.6000
24
4.4444
54
22.5000
25
28.3564
55
100.5786
25
4.8228
55
S3.3410
26
aoxme
56
108.7037
26
5.2160
56
24.1976
27
31.8750
67
106.8750
27
6.^50
57
25.0694
28
33.7037
58
110.0926
28
6.0494
58
25.9667
29
35.5786
59
113.3564
29
6.4891
59
26.8696
30
^.5000
60
116.6666
30
6.9444
60
p
27-7777
1
( CT>- )
BASE 30— SLOPE 1^ to 1.
I
»
1
2
3
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Add.
.6833
1.2222
1.9166
2.6666
a4722
43333
5.2600
6.2222
7.2600
8.3333
9.4722
10.6666
11.9166
13.2222
14.5833
16.0000
17.4722
19.0000
21.5833
22.2222
23.9166
25.6666
27.4722
29.3333
31.2500
33.2222
35.2500
37.3333
39.4722
41.6666
I
31
32
33
34
36
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
69
60
Add.
43.9166
46.2222
48.5833
51.0000
53.4722
66.0000
58.6833
61.22^
63.9166
66.6666
69.4722
72.3333
75.2500
78.2222
81.2500
843333
87.4722
90.6666
93.9166
97.2222
100.5833
1040000
107.4722
111.0000
1145833
118.2222
121.9166
125.6666
129.4722
133.3333
•s
»
1
2
3
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Deduct.
.0092
.0370
.0833
.1480
.2313
.3333
.4537
.6926
.7500
.9259
1.1208
1.3333
1.5648
1.8148
2.0833
2.3704
2.6769
3.0000
3.3426
3.7037
4.0633
4.4815
4.8981
5.3333
5.7869
6.2592
6.7500
7.2592
7.7869
a3333
O •
31
32
33
34
36
36
87
88
39
40
41
42
43
44
45
46
47
48
49
50
61
62
63
54
65
66
57
58
59
60
Deduct.
8.8981
9.4816
10.0833
10.7037
11.3426
12.0000
12.6759
13.3708
14.0833
14.8148
16.6648
16.3333
17.1202
17.9269
18.7600
19.6926
20.4637
21.3333
22.2314
23.1481
24.0833
25.0370
26.0092
27.0000
28.0092
29.0370
30.0833
31.1481
32.2314
33.3333
( CTii. ).
BASE 80— SLOPE U to 1.
1
KM.
1
Add.
Dif. of
Hts.
Dednct.
Dif. of
Hts.
Deduct.
.5879
31
48.3657
1
.0108
31
10.3811
2
1.2407
32
50.9629
2
.0432
32
11.0617
8
1.9583
33
A3.6250
8
.0972
38
11.7638
4
2.7407
34
56.3618
4
.1728
84
12.4876
6
3.5879
35
50.1436
5
.2700
36
13.2330
6
45000
36
62.0000
6
.8889
86
14.0000
7
5.4768
37
64.9218
7
.6293
37
147885
8
6.5185
38
67.9073
8
.6913
88
15.6987
9
7.6260
39
70.9583
9
.8760
39
16.4306
10
8.79^
40
74.0740
10
1.0802
40
17,2889
11
10.0324
41
77.2456
11
1.3071
41
18.1589
12
11.3333
42
80.6000
12
1.6565
42
19.0666
13
12.6990
43
83.8101
13
1.8256
48
19.9747
14
14.1296
44
87.1852
14
2.1173
44
20.9136
16
15.6250
45
90.6250
15
2.4306
45
21.8760
16
17.1852
46
941296
16
2.7654
46
22.8580
17
18.8101
47
97.6990
17
3.1219
47
23.8626
18
20.6000
48
101.3333
18
3.5000
48
248888
19
23.2546
49
105.0324
19
8.8997
49
25.9367
20
24.0740
50
108.7962
20
43210
50
27.0061
21
25.9683
51
112.6260
21
4.7689
51
28.0972
22
27.9073
52
116.6186
22
5.2284
52
29.2098
23
29.9213
53
120.4768
23
5.7145
53
30.3441
24
32.0000
64
124,600J
24
6.2222
64
31.5000
25
34.1435
65
128.5879
25
6.7616
55
32.6774
26
36.3518
56
132.7407
26
7.3024
66
33.8765
27
38.6260
67
186.9583
27
7.8750
57
35.0972
28
40.9629
58
141.2407
28
8.4691
58
86.8894
29
43.3657
69
146.6879
29
9.0648
69
37.6033
30
45.8333
60
150.0000
30
9.7222
60 188.8888
\
( cviii. )
BA8B 80— SLOPE 2 to 1.
1
»
Add.
1,
•s
ta
Add.
1
Deduct.
Dednot.
1
.5926
31
52.8148
.0123
31
11.8642
2
1.2592
82
66.7037
2
.0494
32
12.6419
8
2.0000
88
68.6666
8
.1111
33
13.4444
4
2.8148
34
61.7037
4
.1975
34
14.2716
6
3.7087
86
64.8148
6
.3086
36
16.1234
6
4.6666
3B
68.0000
e
.4444
36
16.0000
7
6.7037
37
71.2592
7
.6049
87
1^9012
8
6.8148
88
74.5926
8
.7901
88
17.8271
9
8.0000
39
78.0000
9
1.0000
39
18.7777
10
9.2592
40
81.4814
10
1.2346
40
19.7630
11
10.5926
41
85.0870
11
1.4938
41
20.7530
12
12.0000
42
88.6666
12
1.7778
42
21.7777
13
13.4814
43
92.3074
13
2.0864
48
22.8271
14
15.0370
44
96.1480
14
2.4197
44
23.9012
15
1&6666
46
100.0000
16
2.7778
46
26.0000
16
18.3704
46
103.9269
16
ai606
46
26.1234
17
20.1480
47
107.9259
17
3.5679
47
27.2716
18
22.0000
48
112.0000
18
4.0000
48
28.4444
19
24.9259
49
116.1480
19
4.4568
49
29.6^20
20
25.9259
60
120.3704
20
4.9882
50
80.8642
21
28.0000
61
124.6666
21
6.4444
51
82.1111
22
30.1480
52
129.0870
22
6.9768
52
33.3827
23
32.3704
63
133.4814
28
a5809
58
34.6790
24
34.6666
64
138.0000
24
7.1111
54
86.0000
25
37.0370
66
1^.5920
26
7.7160
65
37.3456
26
89.4814
66
147.2592
26
8.3457
66
38.7160
27
42.0000
67
152.0000
27
9.0000
57
40.1111
28
44.5926
58
156.8148
28
9.6790
58
41.5308
29
47.2692
59
161.7037
29
10.8827
S9
42.9763
80
50.0000 601
166.6666
80 11.1111 1 60
44.4444
( c«- )
BASE 30-SLOPE 2^ to 1.
€
•a
"Si
^i
3
Add.
S
Add.
Urn
Dednct.
gas
Dednet.
1
.6018
31
61.7130
1
.0154
31
148302
2
1.29^
32
65.1651
2
.0617
%
15.8016
3
2.0833
33
68.7500
3
.1389
33
16.8056
4
2.9630
34
72.4074
4
.2468
34
17.8395
5
8.9352
35
76.1673
6
.3867
36
18.9043
6
5.0000
36
80.0000
6
.5566
86
20.0000
7
ai573
37
83.9352
7
.7561
37
21.1266
8
7.4074
38
87.9630
8
.9876
38
29,.2839
9
a7600
39
92.0638
9
1.2600
39
23.4722
10
10.1851
40
96.2962
10
1.6432
40
24.6918
11
11.7130
41
100.6018
11
1.8673
41
25.9413
12
13.3333
42
105.0000
12
2.2222
42
27.2222
13
15.0462
43
109.4908
13
2.6060
43
28.6360
14
1&8518
44
114.0740
14
3.0247
44
29.8765
15
18.7500
45
118.75(X)
15
a4722
46
31.2600
16
20.7407
46
123.5185
16
a9506
46
32.6643
17
22.8240
47
128.3797
17
44599
47
34.0895
18
25.0000
48
lS3.a333
18
5.0000
48
36.5665
19
28.2665
49
138.3797
19
5.5710
49
87.0524
20
29.6296
50
1445185
20
ai728
50
38.5802
21
32.0833
51
148.7600
21
a8056
51
40.1388
22
34.6296
52
154.0740
22
7.4691
52
41.7283
23
37.2686
53
159.4908
23
8.1636
53
43.3487
24
40,0000
54
166.0000
24
8.8889
54
46.0000
25
42.8240
55
170.6018
26
9.6465
56
4&6820
26
45.7407
56
178.2962
26
10.4321
56
48.8960
27
48.7500
67
182.0833
27
11.2500
67
60.1388
28
51.8518
56
187.9680
28
12.0687
58
51.9185
29.
55.0462
59
193.9352
29
12.9782
59
53.7191
30
58.3333
60
200.0000
30
13.8889
60
65.5666
(ex.)
BASE SO— SLOPE 3 to 1.
}
as
Add.
1
Add.
IKf.of
Hts.
Deduct.
Htt.
Deduct.
1
.6111
31
70.6111
1
.0186
31
17.7963
2
1.3333
32
74.6666
2
.0740
32
ia9630
3
2.1606
33
78.8338
3
.1667
38
20.1666
4
8.1111
34
88.1111
4
.2963
34
21.4074
5
41666
36
87.6000
6
.4628
85
22.6861
6
6.3333
36
92.0000
6
.6667
86
24.0000
7
6.6111
37
96.6111
7
.9074
87
26.3518
8
8.0000
88
101.3383
8
1.1852
88
26.7407
9
9.6000
39
106.1666
9
1.5000
39
28.1666
10
11.1111
40
111.1111
10
1.8518
40
29.6296
11
12.8333
41
116.1666
11
2.2407
41
31.1296
12
14.6666
42
121.3838
12
2.6667
42
32.6666
13
16.6111
48
126.6111
13
8.1296
48
84.2407
14
18.6666
44
132.0000
14
3.6296
44
36.8618
16
20.8333
46
137.6000
16
4.1667
45
37.5000
16
23.1111
46
143.1111
16
4.7407
46
39.1851
17
25.6000
47
149.8333
17
6.3518
47
40.9078
18
28.0000
48
164.6666
18
6.0000
48
42.6666
19
31.6111
49
160.6111
19
6.6862
49
444629
20
83.3333
60
167.6666
20
7.4074
50
46.2963
21
36.1666
61
172.8338
21
8.1667
61
49.1666
22
39.1111
62
179.1111
22
8.9629
62
50.0740
23
42.1666
68
186.6000
28
9.7962
63
62.0186
24
46.3833
64
192.0000
24
10.6667
64
540000
26
48.6111
66
198.6111
26
11.5741
56
66.0184
26
62.0000
66
206.38.33
26
12.5184
56
68.0740
27
66.6000
57
212.1666
27
13.5000
67
60.1666
28
60.1111
58
219.1111
28
14.6186
68
62.2962
29
62.8333
69
226.1666
29
15.6741
59
644620
30
66.6666
60
233.8333
30
1&6667 60
66.6666
( c"- )
BASE 31— SLOPE
; 1 to 1.
M Height
Add.
t
Add.
1
Deduct
Deduct.
.6787
31
22.2463
.0016
31
1.4830
2
1.1666
32
23.1111
2
.0062
32
1.6802
3
1.7689
33
23.9661
3
.0139
33
1.6805
4
2.3703
34
248703
4
.0246
34
1.7839
6
2.9661
36
26.7639
6
.0385
35
1.8904
6
aeiii
36
26.6666
6
.0555
36
2.0000
7
4.2453
87
27.6787
7
.0756
37
2.1126
8
4.8888
38
28.5000
8
•UUOo
38
2.^84
9
6M16
39
29.4305
9
.1250
39
2.3472
10
6.2037
40
30.3703
10
.1643
40
2.4691
11
6.8760
41
31.3194
11
.1867
41
2.6941
12
7.5555
^
32.2777
12
.2222
42
2.7222
13
8.2453
43
33.2463
13
.2608
43
2.8646
14
8.9444
44
34.2222
14
.3026
44
2.9876
15
9.6627
46
35.2083
15
.3472
45
3.1250
16
10.3703
46
36.2037
16
.3951
46
3.2664
17
11.0972
47
37.2083
17
.4460
47
3.4089
18
11.8333
48
38.2222
18
.6000
48
3.6566
19
12.5787
49
39.2463
19
.5571
49
3.7052
20
13.3333
60
40.2777
20
.6173
60
3.8580
21
14.0972
61
41.3194
21
.6805
61
40139
22
14.8703
52
42.3703
22
.7469
52
41728
23
16.6527
63
43.4305
23
.8163
53
43349
24
16.4444
64
44.6000
24
.8889
64
4.6000
25
17.2453
55
46.5787
25
.9647
65
46682
26
18.0556
56
46.6666
26
1.0432
66
48396
27
18.8750
67
47.7639
27
1.1250
67
5.0139
28
19.7037
68
48.8703
28
1.2099
58
5.1913
29
20.5416
59
49.9861
29
1.2978
69
6.3719
30
21.3888
60
51.1111
30
1.3889
60
5.6656
<
( cxii. )
BASE 31— SLOPE
•
; ^ to 1.
}
Add.
1
Add.
if. of
Eits.
Dednot.
3^
Deduct.
»
»
1
&^
1
.5833
31
26.6044
.0031
31
2.9660
2
1.1851
32
27.8518
2
.0123
32
3.3611
9
1.8055
33
29.0277
8
.0278
88
3.6111
4
2.4444
34
30.2222
4
.0494
34
3.5679
5
8.1018
35
31.4862
5
.0772
36
3.7808
6
3.7777
36
32.6666
6
.1111
36
4.0000
7
4.4722
87
33.9166
7
.1512
tn
4.2253
8
5.1851
38
36.1861
8
.1976
88
4.4568
9
5.9166
89
36.4722
9
.2500
89
4.0944
10
6.6666
40
37.7777
10
•OUCtU
40
4.9383
11
7.4352
41
39.1018
11
.8734
41
5.1883
12
8.2222
42
40.4444
12
.4444
42
5.4444
13
9.0277
43
41.8065
13
.6216
43
6.7076
14
9.8518
44
43.1851
14
.6049
44
5.9753
15
10.6944
45
44.6633
15
.6944
45
6.2500
16
11.5665
46
46.0000
16
.7901
46
a5308
17
12.4362
47
47.4351
17
.8920
47
6.8179
18
13.3333
48
48.8888
18
1.0000
48
7.1111
19
14.2600
49
50.3611
19
1.11^
49
7.4106
20
16.1851
50
51.8518
20
1.2346
60
7.7160
21
16.1388
61
53.3611
21
1.3611
61
8.0277
22
17.1111
52
64.8888
22
1.4088
62
8.3456
23
18.1018
53
66.4351
23
1.6327
53
8.6697
24
19.1111
54
68.0000
24
1.7778
64
9.0000
25
20.1388
56
59.5838
25
1.9295
56
9.3364
26
21.1851
56
61.1861
26
2.0864
66
9.6790
27
22.2600
57
62.8055
27
2.2600
57
10.0277
28
23.3333
58
64.4444
28
2.4197
58
10.3827
29
24.4362
59
66.1018
29
2.6966
69
10.7438
30
26.5655
60
67.7777
30
2.7778160
11.1111
( cxiii. )
BASE 31— SLOPE f to 1.
1
.-e
Add.
1
Add.
"Si
Dednet.
2^
■sn
Deduct.
IS
a
o
ft
1
.5880
31
31.1436
1
.0046
31
44490
2
1.2037
32
32.5926
2
.0186
32
47407
8
1.8472
33
34.0694
3
.0416
33
6.0416
4
2.5185
34
35.5740
4
.0740
34
5.8618
5
3.2176
36
37.1066
5
.1167
36
6.6712
6
a9444
36
38.6666
6
.1667
36
6.0000
7
4.6990
37
40.2646
7
.2268
37
6.3379
8
5.4814
38
41.8703
8
.2963
38
6.6861
9
a2916
39
43.6140
9
.8750
39
7.0416
10
7.1296
40
46.1862
10
.4630
40
7.4074
11
7.9954
41
46.8842
11
.5602
41
7.7824
12
8.8888
42
48.6111
12
.6667
42
8.1666
13
9.8102
43
50.3667
13
.7824
43
8.5612
14
10.7692
44
62.1481
14
.9074
44
8.9629
15
11.7360
46
63.9583
15
1.0417
46
9.3750
16
12.7407
46
56.7963
16
1.1852
46
9.7962
17
13.7732
47
57.6620
17
1.3379
47
10.2268
18
14.8333
48
69.6655
18
1.6000
48
10.6666
19
16.9213
49
61.4768
19
1.6713
^
11.1157
20
17.0370
60
63.4260
20
1.8518
50
11.6740
21
18.1805
61
66.4028
21
2.0417
51
12.0416
22
19.3518
62
67.4074
22
2.2407
62
12.5185
23
20.6509
63
69.4397
23
2.4491
53
13.0046
24
21.7777
64
71i»00
24
2.6667
54
13.6000
25
23.0323
55
73.6879
26
2.8935
55
140046
26
24.3147
56
76.7037
26
3.1296
56
146185
27
25.6250
57
77.8472
27
3.3760
57
15.0416
28
26.9629
68
80.0185
28
3.6296
68
15.5740
29
28.3288
59
82.2175
29
3.8936
59
16.1167
30
29.72S»
60
844444
30 1 4.1667
60 16.6666
(cxiv. )
BASE 31— SLOPE 1 to 1.
1
Add.
1
Add.
Dif.of
Hts.
Deduct
Dif.of
Deduct.
.5926
31
35.6926
1
.0062
81
5.9321
2
1.2222
32
37.3333
2
.0247
82
6.3210
3
1.8888
S3
39.1111
3
.0566
83
6.7222
4
2.5926
34
40.9260
4
.0968
34
7.1368
5
3.3333
85
. 42.7777
5
.1643
35
7.5617
6
4.1111
86
446666
6
.2222
86
8.0000
7
49260
87
46.6926
7
.3025
87
8.4606
8
6.7777
38
48.5566
8
.8961
88
8.9135
9
6.6666
89
60.6656
9
.6000
89
9.3888
10
7.6926
40
52.5926
10
.6178
40
9.8766
11
8.5556
41
646666
11
.7460
41
10.3766
12
9.6655
42
66.7777
12
.8889
42
10.8888
13
10.5926
43
58.9260
13
1.0432
43
11.4136
14
11.6666
44
61.1111
14
1.2099
44
11.9506
16
12.7777
46
63.3333
16
1.3889
45
12.6000
16
13.9260
46
65.6026
16
1.5802
46
ia0617
17
16.1111
47
67.8888
17
1.7889
47
13.6868
18
1&3333
48
70.2222
18
2.0000
48
142222
19
17.6926
49
72.6926
19
2.2284
49
148209
20
18.8888
50
75.0000
20
2.4691
60
15.4321
21
20.2222
51
77.4444
21
2.7222
61
16.0555
22
21.6»iM
m
79.9260
22
2.9876
52
16.6918
23
23.0000
63
82.4444
23
3.2664
63
17.3396
24
244444
64
86.0000
24
8.6655
54
18.0000
25
26.9260
66
87.6926
25
3.8630
65
18.6728
26
27.4444
66
90.2222
26
41728
56
19.3560
27
29.0000
57
92.8888
27
45000
ff7
20.0565
28
30.5926
58
96.5926
28
48306
58
20.7664
20
32.2222
69
98.8338
29
5.1913
69
21.4876
30
33.8888
60
101.1111
30
5.5665
60
( <a^- )
BASE 31— SLOPE IJ to 1.
1
Add.
1
Add.
if. of
Hta.
Dednct
3^
Dedsct.
s
!S
o
-
1
.S972
31
40.0416
1
.0077
31
7.4161
2
1.2407
32
42.0740
2
.0809
82
7.9012
8
1.9305
83
44.1528
3
.0694
.33
8.4027
4
2.6666
34
46.2777
4
.1234
84
a9197
5
a4490
86
48.4490
5
.1928
35
9.4621
6
4.2777
86
50.6666
6
.2778
36
10.0000
7
5.1538
37
52.^05
7
.8781
37
10.6632
8
a0740
38
55.2407
8
.'^38
38
11.1419
9
7.0416
39
57.6972
9
.6260
39
11.7361
10
8.0555
40
eaoooo
10
.7716
40
12.8466
11
9.1167
41
62.4490
11
.9336
41
12.9706
12
10.2222
ASl
64.9444
12
1.1111
42
13.6111
13
1L8760
43
67.4862
13
1.3040
43
14.2680
14
12.5740
44
70.0740
14
1.6123
44
14.9382
15
13.8103
45
72.7083
16
1.7861
45
16.6250
16
15.1111
46
76.3888
16
1.9763
46
16.3271
17
16.4490
47
78.1166
17
2.2299
47
17.0447
18
17.8333
48
80.8888
18
2.5000
48
17.7T77
19
19.2640
49
88.7088
19
2.7866
49
18.6262
20
20.7407
50
86.5740
20
8.0864
60
19.2901
21
22.2640
61
89.4862
'21
8.4028
61
20.0694
22
23.8333
52
92.4444
22
3.7846
62
20.8641
23
25.4490
53
95.4490
23
4.0818
63
21.6743
24
27.1111
54
98.6000
24
4.4444
64
22.5000
26
28.8193
65
101.6972
25
4.8228
66
23.8410
26
30.5740
56
104.7407
26
5.2166
66
241975
37
32.8760
67
107.9305
27
6.6260
57
25.0694
28
34.2222
68
111.1666
28
6.0^4
68
25.9667
29
36.1167
69
1144^0
29
6.4891
69
26.8696
30
38.0555
60
117.7777
30
6.9444
60
27.7777
(cxvu)
BASE 81--SL0PE IJ to 1.
2
£
"8 J
% .
B
1
Add.
»
Add.
^1
Dedncb
g«
Dedont.
.6018
31
44.^07
1
.0092
31
8.8981
2
1.2692
32
46.8148
2
.0370
32
9.4815
3
1.975»
33
49.1944
8
.0633
33
10.0883
4
2.7407
34
61.6296
4
.1480
34
10.7037
6
3i!647
36
541203
5
.2313
35
11.3^5
6
AAAAA
36
56.6666
6
.3383
86
12.0000
7
6.3796
37
59.2684
7
.4637
37
12.6769
8
ft8703
38
61.9259
8
.6926
38
13.8708
9
7.4166
39
646388
9
.7500
39
140833
10
8i»186
40
67.4074
10
.9259
40
148148
11
9.6769
41
70.2314
11
1.1208
41
15M48
12
10.8888
42
73.1111
12
1.8333
42
1&8333
13
12.1674
43
76.0462
13
1.5648
43
17.1202
14
13.4816
44
79.0370
14
1.8148
44
17.9269
15
148611
46
82.0833
15
2.0633
45
18.7500
16
16.2962
46
85.1861
16
2.3704
46
19.5926
17
17.7870
47
88.3424
17
2.6769
47
20.4587
18
19.3333
48
91.6655
18
3.0000
48
21.8383
19
20.0360
49
948240
19
ad426
^
22.2314
20
22.6926
50
98.1482
20
a7087
50
23.1481
21
24.3056
61
101.5277
21
40888
61
240833
22
26.0740
52
1049629
22
4.4815
62
26.0370
23
27.8982
53
106.4636
23
48981
63
26.0092
24
29.7777
54
112.0000
24
5.3333
64
27.0000
25
31.7130
65
115.6018
26
5.7869
56
28.0092
26
33.7037
56
119.2692
26
6.2692
56
29.0370
27
36.7600
57
122.97^
27
6.7500
57
30.0833
28
37.8618
68
126.7407
28
7.2592
58
81.1481
29
40.0092
69
130i>647
29
7.7869
59
32.2314
80
42.2222 60
1344444
30
8.8333
60
88.8383
( cxvii. )
BASE 81— SLOPE If to 1.
1
m
Add.
1
Add.
Dif.of
Hts.
Deduct.
Dif.of
Hts.
Deduct.
1
.6064
31
48.9998
1
.0108
31
10.8811
2
1.2777
32
61.5665
2
.0432
32
11.0617
3
2.0189
33
542860
3
.0972
88
11.7638
4
2.8148
34
5&9815
4
.1728
84
12.4876
5
a6804
35
59.7916
5
.2700
85
18.2330
6
4.6111
36
62.6666
6
.3889
36
140000
7
5.6064
87
65.6064
7
.5293
37
147885
8
6.6666
88
68.6111
8
.6913
38
16.5987
9
7.7916
89
71.6804
9
.8760
39
16.4305
10
8.9815
40
74.8148
10
1.0802
40
17.2839
11
10.2360
41
78.0139
11
1.3071
41
18.1689
12
11.5556
^
81.2777
12
1.5566
^
19.0565
18
12.9398
43
84.6064
13
1.8266
43
19.9747
14
143888
44
88.0000
14
2.1173
44
20.9185
Id
15.9027
46
91.4583
15
2.4306
45
21.8760
16
17.4815
46
94.9814
16
2.7664
46
22.8580
17
19.1260
47
98.5694
17
8.1219
47
23.8626
18
20.8333
48
102.2222
18
3.5000
48
24.8888
19
22.6064
49
105.9397
19
3.8997
49
25.9367
20
24.4444
60
109.7222
20
4.3210
50
27.0061
21
2&8470
61
118.5694
21
47639
61
28.0972
22
28.3147
62
117.4814
22
5.2284
52
29.2098
28
30.3470
58
121.4683
23
6.7146
53
30.8441
24
32.4444
64
126.5000
24
6.2222
64
81.5000
25
34.6064
56
129.6064
25
a7616
55
82.6774
26
d&8833
56
133.7777
26
7.3024
66
33.8766
27
89.1250
67
138.0140
27
7.8760
67
35.0972
28
41.4815
58
142.3148
28
8.4691
68
86.3394
29
43.9027
59
146.6804
29
9.0848
59
87.6033
80
46.8888
60
161.1111
80
9.7222
60
38.8888
■■; " " ■ ' - .-_,T., . ■ . -
( cxTiii. )
BASE 31— SLOPE 2 to 1.
i
m
1
Add.
1
m
Add.
Dif.of
Hts.
Deduct
Dif.of
Uts.
Deduct
.6111
31
53.3888
1
.0123
81
11.8642
2
1.2962
82
66.2962
2
.0494
32
12.6419
8
2.0556
33
69.2777
8
.1111
33
ia4444
4
2.8888
34
62.8838
4
.1976
84
142716
5
a7962
36
65.4629
5
.3086
36
15.1234
6
4.7777
86
68.6666
6
.4444
36
16.0000
7
5.8383
37
71.9444
7
.6049
37
16.9012
8
6.9629
88
76.2962
8
.7901
38
17.8271
9
8.1666
39
78.7222
9
1.0000
39
18.7777
10
9.4444
40
82.2222
10
1.2346
40
19.7580
11
10.7962
41
85.7962
11
1.^38
41
20.7580
12
12.2222
^
89.4444
12
1.7778
42
21.7777
13
13.7222
48
93.1666
13
2.0864
43
22.8271
14
15.2962
44
96.9^29
14
2.4197
44
23.9012
15
16.9444
46
100.8338
16
2.7778
45
26.0000
16
18.6666
46
1047777
16
3.1605
46
26.1234
17
20.4629
47
108.7962
17
3.5679
47
27.2716
18
22.3333
48
112.8888
18
40000
48
28.4444
19
242777
^
117.0656
19
44668
49
29.6420
20
26.2962
50
121.2962
20
49382
60
30.86^
21
2ad888
51
126.6111
21
6.4444
51
82.1111
22
30.5656
62
130.0000
22
6.9758
52
33.8827
23
32.7962
68
1344629
28
6.5309
53
84.6790
24
35.1111
64
139.0000
24
7.1111
54
36.0000
26
37.6000
55
148.6111
26
7.7160
56
37.8466
26
39.9629
66
14a2962
26
8.8467
66
38.7160
27
42.6000
67
163.0556
27
9.0000
67
40.1111
28
45.1111
58
167.8888
28
9.6790
58
41.6308
29
47.7962
69
162.7962
29
10.8827
69
^9758
80 160.5555
60
167.7777
80
11.1111
60
44.4444
( cziz. )
BASE 31— SLOPE 2( to 1.
1
-8
Add.
1
Add.
if. of
Hti.
Dedaet.
if. of
Hti.
Deduct.
a
m
o
P
1
.6208
31
62.2870
1
.0154
81
148302
2
1.3883
82
65.7777
2
.0617
32
16.8013
3
2.1388
33
69.8611
3
.1889
33
16.8056
4
a0370
34
73.0870
4
.2468
84
17.8895
5
4.0277
35
7&8055
5
.3857
35
18.9048
6
5.1111
36
c5U.tJduD
6
.5555
36
20.0000
7
&2870
37
84.6202
7
.7561
87
21.1265
8
7.55S5
38
oo.UIdo
8
.9676
38
22.2839
9
8.9166
39
92.8055
1.2500
39
28.4722
10
10.8708
40
97.0370
10
1.54%
40
246918
11
11.9166
41
101.8611
11
1.8673
41
25.9413
12
ia5555
^
105.7777
12
2.2222
4@
27.2222
13
15.2870
43
110.2870
13
2.6080
48
28.6860
14
17.1111
44
1148888
14
3.0247
44
29.8765
15
19.0277
45
119.5883
15
3.4722
45
31.2500
16
21.0870
46
124.3708
16
8.9506
46
32.6643
17
23.1388
47
129.2500
17
44599
47
840896
18 125.3833
19 127.6208
48
1342222
18
5.0000
48
35.5665
49
139.2870
19
5.6710
49
37.0524
20
30.0000
50
1444444
20
6.1728
60
38.6802
21
34.4722
51
149.6944
21
6.8055
51
40.1388
22
35.0370
62
155.0870
22
7.4691
52
41.7283
23
37.6944
63
160.4722
23
8.1686
63
43.3487
24
40.4444
54
166.0000
24
8.8889
54
45.0000
25
43.2870
55
171.6208
25
9.6455
56
46.6820
26
46.2St22
56
177.8338
26
10.4321
66
48.3950
27
^.2500
57
183.1388
27
11.2500
57
50.1888
28
62.3708
58
189.0370
28
12.0587
68
51.9136
29
55.5833
69
195.0277
29
12.9782 59
53.7191
ao
58.8888
60
201.1111
80
18.8889 60 65.6555
( c«- )
BASE 81— SLOPE 3 to 1.
:c
Add.
i
a
Add.
1
Dodnct.
■Si
Deduct.
1
.6296
31
71.1851
.0185
31
17.7963
2
1.3704
32
75.2592
2
.0740
32
18.9630
3
2.2222
33
79.4444
3
.1667
33
20.1666
4
3.1851
34
83.7407
4
.2963
34
21.4074
6
4.2592
35
88.1481
6
.4628
35
22.6851
6
5.4444
36
92.6066
6
.6667
36 1240000 1
7
a7407
37
97.2962
7
.9074
87
25.3518
8
8.1481
38
102.0370
8
1.1852
38
2&7407
9
9.6666
39
106.8888
9
1.5000
39
28.1666
10
11.2962
40
111.8518
10
1.8518
40
29.6296
11
13.0370
41
116.9260
11
2.2407
41
31.1296
12
148888
42
122.1111
12
2.6667
42
32.6666
13
16.8518
43
127.4074
13
3.1296
43
342407
14
18.9260
44
132.8146
14
3.6296
44
35.8518
15
21.1111
45
138.3333
15
41667
45
37.5000
16
23.4074
46
143.9629
16
47407
46
39.1851
17
25.8147
47
149.7037
17
5.3518
47
40.9074
18
28.3333
48
155.5555
18
6.0000
48
42.6666
19
30.9629
4d
161.5185
19
&6852
49
44.4629
20
33.7037
50
167.5926
20
7.4074
50
46.2963
21
36.5555
51
173.7777
21
8.1667
51
49.1666
22
39.5185
52
180.0740
22
8.9629
52
50.0740
23
42.5926
53
186.4814
23
9.7962
53
52.0185
24
45.7777
54
193.0000
24
10.6667
54
540000
25
49.0740
55
199.6296
25
11.5741
55
56.0184
26
52.4814
56
20&3703
26
12.5184
56
58.0740
27
56.0000
57
213.2222
27
13.5000
67
60.1666
28
59.6296
58
220.1852
28
145185
58
62.2962
29
63.3703 59
227.2592
29
15.5741 59 1
64.4629
30
67.2222 60 234.4444
30 16.66671 60 f
6&6666
1
( cxxi. )
BASE 32— SLOPE i to 1.
Add.
i
Add.
"A
Deduct.
1
Deduct
1
X
1
31
.5972
81
22-8194
.0015
1.4830
2
1.2037
82
23.7037
2
.0062
82
1.5802
3
1.8194
33
245972
3
.0139
33
1.6805
4
2.4444
34
25.5000
4
.0246
34
1.7839
5
3.0787
35
26.4120
6
.0886
36
1.8904
6
8.7-222
36
27.3333
6
.0556
86
2.0000
7
4.3750
37
28.2639
7
.0756
37
2.1126
1
8
5.0370
38
29.2037
8
.0988
88
2.2284
9
6.7083
39
30.1527
9
.1250
39
2.3472
10
6.3888
40
81.1111
10
.1643
40
2.4691
11
7.0787
41
82.0787
11
.1867
41
2.5941
12
7.7777
42
38.0555
12
.2222
42
2.7222
13
8.4861
43
34.0416
13
.2608
43
2.8545
14
9.2037
44
36.0370
14
.3025
44
2.9876
15
9.9305
45
86.0416
15
.3472
45
3.1250
16
10.6666
46
87^0555
16
.3961
46
3.2654
17
11.4120
47
88.0787
17
.4460
47
3.4089
18
12.1666
48
39.1111
18
.6000
48
S.5555
19
12.9305
49
40.1527
19
.6571
49
3.7052
20
13.7037
50
41.2037
20
.6173
60
a8580
21
14.4861
51
42.2639
21
.6805
51
4.0139
22
15.2777
52
43.8333
22
.7469
62
4.1728
23
16.0787
53
44.4120
23
.8163
63
4.3349
24
16.8888
54
46.5000
24
.8889
54
4.5000
25
17.7083
55
46.6972
26
.9647
65
4.6682
26
18.5370
56
47.7037
26
1.0432
56
4.8395
27
19.3750
67
48.8194
27
1.1260
57
5.0139
28
20.2222
68
49.9444
26
1.2099
58
5.1913
29
21.0787
69
51.0787
29
1.2978
69
6.3719
30
21.9444
60
52.2222
80
1.8889
60
6.5555
■
R
( cxxii. )
BASE 3^-SLOPE ^ to 1.
1
1
Add.
1
S
31
Add.
I>if.of
Dednet
Deduct.
.6018
27.2685
1
.0031
31
2.9660
2
1.2222
32
28.4444
2
.0123
32
3.1605
3
1.8611
33
29.6389
3
.0278
S3
33611
4
2.6185
34
30.8618
4
.0494
34
3.5679
5
3.1944
35
32.0833
6
.0772
35
3.7808
6
a8888
36
33.3333
6
.1111
86
4.0000
7
4.6018
37
34.6018
7
.1612
37
4.2253
8
5.3333
38
36.8888
8
.1975
38
4.4568
9
6.0833
39
37.1944
9
.2500
39
4.6944
10
6.8518
40
38.6185
10
•oOoo
40
4.9383
11
7.6389
41
39.8611
11
.3734
41
5.1883
12
8.4444
42
41.2222
12
.4444
42
6.4444
13
9.2685
43
42.6018
13
.5216
43
6.7067
14
10.1111
44
44.0000
14
.6049
44
5.9763
16
10.9722
46
45.4166
16
.6944
45
6.2500
16
11.8518
46
46.8518
16
.7901
46
6.5308
17
12.7600
47
48.3a35
17
.8920
47
6.8179
18
13.6666
48
^.7777
18
1.0000
48
7.1111
19
14.6018
49
61.2684
19
1.1142
49
7.4106
20
15.5556
60
52.7777
20
1.2346
50
7.7160
21
16.5277
51
643056
21
1.3611
51
8.0277
22
17.6186
62
66.8518
22
1.4938
62
8.3466
23
18.5277
63
67.4166
23
1.6327
63
8.6607
24
19.5656
64
69.0000
24
1.7778
64
9.0000
25
20.6018
55
60.6018
26
1.9296
55
9.3364
26
21.6666
66
62.2222
26
2.0864
66
9.6790
27
22.7600
57
63.8611
27
2.2500
57
10.0277
28
23.8618
58
65.5185
28
2.4197
68
10.3827
29
24.9722
59
67.1944
29
2.5956
59
10.7438
30
2ailll
60
68.8888
30
2.7778
60
11.1111
1
( cxxiii. )
BASE 32— SLOPE | to 1.
t
Add.
•t
Add.
"a
Deduct.
Jaaa
Dednct.
»
a
31
0*
1
^^ p*^
1
.6064
31.7176
.0046
31
4.4490
2
1.2407
32
33.1851
2
.0185
32
4.7407
3
1.9028
33
34.6805
3
.0416
33
5.0416
4
2.5926
34
36.2037
4
.0740
34
5.3618
5
3.3101
35
37.7846
5
.1157
36
66712
6
40555
36
39.3333
6
.1667
86
6.0000
7
4.8286
37
40.9397
7
.2268
37
63379
8
5.6296
38
42.5740
8
.2963
38
6.6851
9
6.4583
39
44.2360
9
.3750
39
7.0416
10
7.3148
40
45.9259
10
.4630
40
7.4074
11
8.1991
41
47.6435
11
.6602
41
7.7824
12
9.1111
42
49.3888
12
.6667
42
8.1666
13
10.0509
43
51.1620
13
.7824
43
8.6602
14
11.0185
44
52.9629
14
.9074
44
89629
15
12.0138
45
54.7916
15
1.0417
46
9.3750
16
13.0370
46
56.6481
16
1.1852
46
9.7962
17
14.0879
47
58.S323
17
1.3379
47
10.2268
18
15.1666
48
60.4444
18
1.5000
48
10.6666
19
16.2731
49
62.3842
19
1.6713
49
11.1157
20
17.4074
50
64.3518
20
1.8518
50
11.6740
21
18.5694
51
66.3472
21
2.0417
51
12.0416
22
19.7692
52
68.3703
22
2.2407
62
12.5186
23
20.9768
53
70.4212
23
2.4491
53
13.0046
24
22.2222
54
72.5000
24
2.6667
64
13.5000
25
23.4953
55
74.6064
25
2.8935
65
14.0046
26
24.7962
56
76.7407
26
3.1296
66
14.5185
27
26.1260
57
78.9028
27
8.3750
57
15.0416
28
27.4814
58
81.0926
28
3.6296
68
15.6740
29
28.8657
59
83.3101
29
3.8935
59
16.1157
30
30.2777
60
85.5555
30
4.1667 1 60
lft6666
1
•
( cxxiv. )
BASE Sa— SLOPE 1 to 1.
Add.
1
Add.
Dedoct
ssas
Deduct.
03
»
a*"
1
a
1
.6111
31
36.1666
.0062
31
6.9321
2
1.2592
32
37.9259
2
.0247
32
6.321U
3
1.9444
33
39.7222
3
.0565
33
6.7222
4
2.6666
94
41.5555
4
.0988
34
7.1358
5
3.4259
35
43.^^59
6
.1643
36
7.6617
6
4.2222
36
45.3333
6
.2222
36
8.0000
7
5.0555
37
47.2777
7
.3025
37
8.4506
8
5.9259
38
49.2592
8
.3951
38
8.9135
9
6.8333
39
51.2777
9
.5000
39
9.3888
10
7.7777
40
53.3333
10
.6173
40
9.8765
11
8.7592
41
55.4259
11
.7469
41
10.3765
12
9.7777
42
57.5655
12
.8889
42
10.8888
13
10.8333
43
69.7222
13
1.0432
48
11.4135
14
11.9259
44
61.9259
14
1.2099
44
11.9606
16
13X)555
45
64.1666
15
1.3889
46
12JS000
16
14.2222
46
66.4444
16
1.6802
46
ia0617
17
15.4259
47
68.7692
17
1.7839
47
13.6358
18
16.6666
48
71.1111
18
2.0000
48
142222
19
17.9444
4l»
73.6000
19
2.2284
49
14.8-209
20
19.2592
50
75.9259
20
2.4691
50
16.4321
21
20J6111
51
78.3888
21
2.7222
51
16.0555
22
22J0OOO
52
80.8888
22
2.9876
52
16.6913
23
23.4259
53
83.4259
23
3.2654
6d
17.3396
24
24.8888
54
86.0000
24
3.5556
54
18.0000
25
26.3888
55
88.6111
26
3.8580
56
18.6728
26
27.9259
56
91.2592
26
4.1728
66
19.3580
27
29.5000
57
93.9444
27
4.5000
67
20.0556
28
31.1111
58
96.6666
28
4.8395
68
20.7664
29
32.7592
59
99.4250
29
5.1913
59
21.4876
30
34.4444 60
102.2222
80 5.65551
60
22.2222
( CXXY. )
BASE 32— SLOPE IJ to 1.
Add.
Add.
I
Deduct.
Dif.of
Hta.
Dednct.
1
.6157
31
40.6157
.0077
31
7,4151
2
1.2777
32
42.6666
2
.0309
32
7.9012
3
1.9861
33
44.7639
3
.0694
33
8.4027
4
2,7407
34
46.9074
4
.1234
34
8.9197
5
3.5416
35
^.0971
6
.1928
35
9.4521
6
4.3888
36
61.3333
6
.2778
36
10.0000
7
5.2823
37
53.6167
7
.3781
37
10.5632
8
6.2222
38
66.9444
8
.4938
38
11.1419
9
7.2083
39
58.3195
9
.6260
39
11.7361
10
8.2407
40
60.7407
10
.7716
40
12.3456
11
9.3195
41
63.2083
11
.9336
41
12.9706
12
10.4444
42
65.7222
12
1.1111
42
13.6111
13
11.6157
43
68.2823
13
1.3040
43
14.2680
14
12.8333
44
70.8888
14
1.5123
44
14.9382
15
14.0971
45
73.5416
15
1.7361
46
16.^50
16
16.4074
46
76.2407
16
1.9753
46
16.3271
17
16.7639
47
78.9861
17
2.2299
47
17.0447
18
18.1666
48
81.7777
18
2.5000
48
17.7777
19
19.6167
49
84.6167
19
2.7866
49
18.5262
20
21.1111
50
87.6000
20
3.0864
60
19.2901
21
22.6528
61
90.4305
21
3.4028
61
20.0694
22
24.2407
52
93.4074
22
3.7346
62
20.8641
23
25.8760
53
96.4305
23
4.0818
63
21.6743
24
27.5655
54
99.5000
24
4.4444
54
22.5000
26
29.2823
56
102.6157
26
4.8228
65
23.3410
26
31.0556
56
106.7777
26
6.2160
56
24.1976
27
32.8750
67
108.9861
27
5.^50
67
26.0694
28
34.7407
58
112.2407
28
6.0494
58
25.9567
29
36.662&
69
115.5416
29
6.4891
69
26.8696
30
38.6111
60
118.8888
80
6.9444
60
27.7777
J,
L^
( cxxvi. )
BASE 32— SLOPE IJ to 1.
•8
Add.
1
Add.
Oednct.
Dedact.
S
s
a*
1
Q*
1
.6203
31
45.0648
.0092
31
8.8981
2
1.2962
32
47.4074
2
.0370
32
9.4816
3
2.0277
33
49.8055
3
.0833
38
10.0838
4
2.8148
34
52.2592
4
.1480
34
10.7037
6
3.6574
35
,54.7685
5
.2313
35
11.3425
6
4.5555
86
57.3833
6
.3333
36
12.0000
7
5.5092
37
59.9536
7
.4537
37
12.6759
8
6.5185
38
62.6296
8
.5926
38
13.8708 .
9
7.5833
39
65.3611
9
.7600
39
14.0888
10
8.7037
40
68.1481
10
.9269
40
14.8148
11
9.8797
41
70.9907
11
1.1203
41
16.5648
12
11.1111
42
73.8888
12
1.3333
42
16.3833
13
12.3981
43
76.8425
13
1.5648
43
17.1202
14
13.7407
44
79.8519
14
1.8148
44
17.9259
15
15.1388
45
82.9166
15
2,0833
45
18.7600
16
16.5926
46
86.0370
16
2.3704
46
19.6925
17
18.1018
47
89.2129
17
2.6759
47
20.4537
18
19.6666
48
92.4444
18
3.0000
48
21.3333
19
21.2870
49
95.7314
19
3.3426
49
22.2314
20
22.9629
50
99.0740
20
3.7037
50
23.1481
21
24.6944
61
102.4722
21
4.0833
61
24.0833
22
26.4814
52
105.9259
22
4.4816
52
25.0370
23
28.3241
63
109.4351
23
4.8981
53
26.0092
24
30.2222
54
113.0000
24
6.3333
64
27.0000
25
32.1758
55
116.6203
25
5.7869
55
28.0092
26
34.1851
56
120.2962
26
6.2592
56
29.0370
27
36.2500
57
124.0277
27
6.7500
67
30.0833
28
38.3703
58
127.8148
28
7.2692
58
31.1481
•29
40.5462
59
131.6674
29
7.7869
59
32.2314
30
42.7777
60
135.5655
30
8.33a3
60
33.3333
( CXZTli. )
BASE 32— SLOPE If to 1.
4^
t
Add.
•r
Add.
Deduct.
if. of
Deduct.
1
»
Q*
Q"
.6250
31
49.5139
1
.0108
31
10.3811
2
1.3147
32
62.1481
2
.0432
32
11.0617
3
2.0694
33
54.8472
3
.0972
33
11.7638
4
2.8888
34
57.6111
4
.1728
34
12.4876
5
3.7731
36
60.4397
6
i»00
35
13.2330
6
4.7222
36
63.3333
6
.3889
36
14.0000
7
5.7360
37
66.2916
7
.5293
37
14.7885
8
6.8148
38
69.3148
8
.6913
38
16.5987
9
7.9588
39
72.4027
9
.8760
39
16.4305
10
9.1666
40
75.5556
10
1.0802
40
17.2839
11
10.4399
41
78.7731
11
1.3071
41
18.1689
12
11.7777
42
82.0665
12
1.6555
^
19.0655
13
13.1805
43
85.4027
13
1.8256
43
19.9747
14
14.6481
44
88.8148
14
2.1173
44
20.9136
16
16.1805
45
92.2916
16
2.4305
45
21.8750
16
17.7777
46
96.8333
16
2.7654
46
22.8580
17
19.4399
47
99.4397
17
3.1219
47
23.8626
18
21.1666
48
103.1111
18
3.5000
48
248888
19
22.9583
49
106.8472
19
3.8997
49
25.9367
20
24.8148
60
110.6481
20
4.8210
60
27.0061
21
26.7360
61
114.5139
21
4.7639
61
28.0972
22
28.7222
62
118.4444
22
6.2284
52
29.2098
23
30.7731
63
122.4399
23
5.7145
53
30.3441
24
32.8888
54
126.500J
24
6.2222
64
31.5000
25
36.0694
55
130.6250
26
6.7516
65
32.6774
26
37.3147
66
1348147
26
7.3024
56
33.8765
27
39.6260
57
139.0694
27
7.8750
57
35.0972
28
^0000
58
143.3888
28
8.4691
58
36.3394
29
44.4399
69
147.7731
29
9.0848 59
37.6033
30
46.94441 60
*
152.2222
30
9.7222 60
38.8888
( cxxviii. )
BASE 32— SLOPE 2 to 1.
1
Add.
1
Add.
if. of
Ht8.
Dedact.
Deduct.
ffi
31
•
1
31
1
.6296
53.9629!
,0123
11.8642
2
1.3333
32
56.8888
2
.0494
32
12.6419
3
2.1111
33
59.8888
3
.1111
33
13.4444
4
2.9629
34
62.9629
4
,1975
84
14.2716
5
3.8888
35
66.1111
5
.3086
35
15.1234
6
4.8888
36
69.3833
6
.4444
86
16.0000
7
6.9629
37
72.6296
7
.6049
37
16.9012
8
7.1111
38
76.0000
8
.7901
88
17.8271
9
8.3333
39
79.4444
9
1.0000
39
18.7777
10
9.6296
40
82.9629
10
1.2346
40
19.7530
11
11.0000
41
86.5555
11
1.4936
41
20.7530
12
12.4444
42
90.2222
12
1.7778
42
21.7777
13
13.9629
43
93.9629
13
2.0864
43
22.8271
14
15.6565
44
97.7777
14
2.4197
44
23.9012
16
17.2222
45
101.6666
15
2.7778
45
25.0000
16
18.9629
46
105.6296
16
3.1605
46
26.1234
17
20.7777
47
109.6666
17
3.5679
47
27.2716
18
22.6666
48
113.7777
18
4.0000
48
28.4444
19
24.6296
49
117.9629
19
4.4568
49
29.6420
20
26.6666
50
122.2222
20
4.9882
60
30.8642
21
28.7777
61
126.5555
21
5.4444
61
32.1111
22
30.9629
52
130.9629
22
5.9753
62
33.3827
23
33.2222
53
135.4444
23
6.6309
53
34.6790
24
35.5555
54
140.0000
24
7.1111
54
36.0000
26
37.9629
55
144.6296
25
7.7160
65
37.3456
26
40.4444
56
149.3333
26
8.3467
56
38.7160
27
43.0000
57
154.1111
27
9.0000
67
40.1111
28
45.6296
58
158.9629
28
9.6790
58
41.5308
29
48.3333
59
163.8888
29
10.3827
69
42.9753
30
51.1111
60
168.8888
30
11.1111
60
44.4444
( cxxix. )
BASE 32— SLOPE 2j^ to 1.
•8
Add.
•**
t
Add.
if. of
Deduct.
if. of
Hts.
Dedaet.
S
1
SB
Q
Q
.6388
31
62.8611
1
.0154
31
14.8302
2
1.3703
32
66.8703
2
.0617
32
16.8016
3
2.1944
33
69.9722
3
.1389
33
16.8055
4
3.1111
34
7^6666
4
.2468
34
17.8395
5
41203
35
77.4637
6
.3867
36
18.9043
6
5.2222
36
81.3333
6
.5665
36
20.0000
7
6.4166
37
85.3055
7
.7661
87
21.1265
8
7.7087
38
89.3703
8
.9876
38
22.2839
9
9.0833
39
93.5277
9
1.2600
39
23.4722
10
10.5555
40
97.7777
10
1.5432
40
24.6913
11
12.1203
41
102.1203
11
1.8673
41
25.9418
12
13.7777
42
106.5555
12
2.2222
42
27.2222
13
15.5-^77
43
111.0833
13
2.6080
43
28.6360
14
17.3703
44
116.7037
14
3.0247
44
29.8766
Id
19.3055
45
120.4166
15
3.4722
45
31.2600
16
21.3333
46
125.2222
16
3.9506
46
32.6648
17
23.4537
47
130.1203
17
4.4699
47
34.0895
18
25.6666
48
135.1111
18
5.0000
48
35.5666
19
27.9722
49
140.1944
19
5.6710
49
37.0624
20
30.3703
60
146.3703
20
6.1728
50
38.5802
21
32.8611
51
150.6388
21
6.8065
61
40.1388
22
35.4444
62
156.0000
22
7.4691
52
41.7283
23
38.1203
53
161.4637
23
8.1636
53
43.3487
24
40.8888
54
167.0000
24
8.8889
54
45.0000
25
43.7500
55
172.6388
25
9.6456
66
46.6820
26
46.7037
56
178.3703
26
10.4321
66
48.3960
27
49.7500
57
184.1944
27
11.2600
57
60.1388
28
52.8888
58
190.1111
28
12.0587
68
51.9135
29
66.1203
59
196.1203
29
12.9782
69
63.7191
30
59.4444
60
202.2222
30
13.8889
60
s
65.6666
( cxxx. )
BASE 32— SLOPE 3 to 1.
1
Add.
1
Add.
if. of
Bts.
Dednct.
°i
rax
Deduct.
v
BB
Q
a
1
.6480
31
71.7692
1
.0186
31
17.7963
2
1.4074
32
75.8618
2
.0740
32
18.9630
3
2.2777
33
80.0565
3
.1667
33
20.1666
4
3.2592
34
843703
4
.2963
34
21.4074
6
43518
35
88.7962
6
.4628
35
22.6861
6
5.5555
36
93.3333
6
.6667
36
240000
7
6.8703
37
97.9814
7
.9074
37
25.3518
8
8.2962
38
102.7407
8
1.1852
38
26.7407
9
9.8333
39
107.6111
9
1.5000
39
28.1666
10
11.4814
40
112.6926
10
1.8518
40
29.6296
11
13.2407
41
117.6851
11
2.2407
41
31.1296
12
15.1111
42
122.8888
12
2.6667
42
32.6666
13
17.0926
43
128.2037
13
3.1296
43
34.2407
14
19.1851
44
133.6296
14
3.6296
44
35.8518
15
21.3888
45
139.1666
15
41667
45
37.5000
16
23.7037
46
1448148
16
47407
46
39.1851
17
26.1296
47
150.6740
17
6.3518
47
40.9078
18
28.6666
48
156.4444
18
6.0000
48
42.6666
19
31.3148
49
162.4269
19
6.6862
49
44.4629
20
34.0740
50
168.6185
20
7.4074
50
46.2963
21
36.9444
61
1747222
21
8.1667
51
49.1666
22
39.9259
62
181.0370
22
8.9629
62
50.0740
23
43.0185
63
187.4^29
23
9.7962
63
62.0185
24
46.2222
54
194.0000
24
10.6667
64
540000
25
49.5370
55
200.6480
25
11.5741
56
66.0184
26
52.9629
66
207.4074
26
12.5184
66
58.0740
27
56.5000
67
2142777
27
13.6000
57
60.1666
28
58.1480
68
221.2592
28
146185
58
62.2962
29
63.9074
59
228.3618
29
15.5741
69
64.4629
30
67.7777
60
235.6566
30
16.6667
60
66.6666
( cxxxi. )
BASE 33-8LOPE i to 1.
4^
•s
Add.
i
•
Add.
if. of
Dednct.
3^
Deduct.
a
X
O
Q
1
.6157
31
23.3935
1
.0016
31
1.4830
2
1.2407
32
24.2963
2
.00^
32
1.6802
3
1.8760
33
26.2083
3
.0139
33
1.6806
4
2.5185
34
2ai296
4
.0246
34
1.7830
5
3.1713
35
27.0601
5
.0386
35
1.8904
6
3.8333
36
28.0000
6
.0655
36
2.0000
7
4.5046
37
28.9^0
7
.0766
37
2.1126
8
5.1862
38
29.9074
8
.0988
38
2.2284
9
5.8750
39
30.8760
9
.1250
39
2.3472
10
6.5740
40
31.8619
10
.1543
40
2.4691
11
7.2824
41
32.8379
11
.1867
41
2.6941
12
8.0000
42
33.8333
12
.2222
42
2.7222
13
8.7268
43
34.8379
13
.2608
43
2.8645
14
9.4629
44
36.8619
14
.3026
44
2.9876
15
10.2083
46
36.8760
15
.3472
45
3.1260
16
10.9629
46
37.9074
16
.3951
46
3.2654
17
11.7-268
47
38.9940
17
.4460
47
3.4089
18
12.5000
48
40.0000
18
.6000
48
3.6566
19
13.2824
49
41.0601
19
.6671
49
3.70^
20
14.0740
60
42.1296
20
.6173
60
3.8680
21
14.8760
51
43.2083
21
.6806
61
4.0139
22
15.6862
62
44.2963
22
.7469
52
4,1728
23
16.5046
63
46.3935
23
.8163
53
4.33^
24
17.3333
64
46.5000
24
.8889
54
45000
25
18.1713
65
47.6157
26
.9647
55
4.6682
26
19.0185
66
48.7407
26
1.0432
66
48395
27
19.8760
67
49.8760
27
1.1250
67
6.0139
28
20.7407
68
61.0186
28
1.2099
58
6.1913
29
21.6167
59
62.1713
29
1.2978
59
6.3719
30 22.50001
60
53.3333
30
1,3889
60
6.6655
( cxxxii. )
•
BASE 33— SLOPE
1 ^ to 1.
1
Add.
1
Add.
[Si
Deduct.
if. of
Bts.
Dedact.
•
,«
to
ft
ft
31
1
.6203
31
27.8426
1
.0031
2,9660
2
1.2592
32
29.0370
2
.0123
32
3,1605
3
1.9166
33
30.2500
8
.0278
33
3,3611
4
2.5926
34
31.4815
4
.0494
34
8.5679
6
3.2870
35
32/7814
5
.0772
35
3,7808
6
40000
36
340000
6
.1111
36
40000
7
4.7314
37
35.2870
7
.1512
37
42253
8
5.4815
38
36,5926
8
.1975
38
44568
9
6.2500
39
37.9166
9
.2500
39
4,6944
10
7.0370
40
39.2592'
1
10
.3086
40
49383
11
7.8^6
41
40.6203
11
.3734
41
5.1883
12
8.6666
42
42.0000
12
AAAA
• J. X X'X
42
5.4444
13
9.5092
43
43.3981
13
.5216
43
6,7076
14
10.3703
44
44.8148
14
.6049
44
5.9763
15
12.2500
45
46.2500
15
.6944
45
6.2500
16
12.1481
46
47.7037
16
.7901
46
6.5308
17
13.0647
47
49.1758
17
.8920
47
6.8179
18
14.0000
48
50.6666
18
1.0000
48
7.1111
19
14,9537
49
52.1758
19
1.1142
49
7.4105
20
15.9259
50
53.7037
20
1.2346
50
7.7160
21
16.9166
51
55.2500
21
1.3611
51
8.0277
22
17.9269
52
56.8148
22
1.4938
52
8.3456
23
18.9537
53
58.3981
28
1.6327
53
8,6697
24
20.0000
54
60.0000'
24
1.7778
64
9,0000
25
21.0647
55
61.6203
25
1.9295
65
9.3364
26
22.1481
56
63.2592 '
26
2.0864
56
9.6790
27
23.2500
57
64.9166
27
2.2500
57
10.0277
28
24.3703
58
66.5926
28
2.4197
68
10.3827
29
25.50^2
59
68.2870
29
2,5956
59
10.7438
30
26.6666
60
70.0000'
30
2,7778
•
60 11,1111
•
( cxxxiii. )
BASE 33— SLOPE } to 1.
4^
-a,
Add.
1
Add.
if. of
Deduct.
if. of
Hts.
Deduct.
1
X
1
•
31
.6250
31
32.2916
.0046
44490
2
1.2777
32
33.7777
2
.0185
32
4.7407
3
1.9583
33
36.2916
3
.0416
33
5.0416
4
2.6666
34
36.8333
4
.0740
34
6.3618
5
3.4027
36
38.4027
6
.1167
36
6.6712
6
4.1666
36
40.0000
6
.1667
36
6.0000
7
4.9583
37
41.6250
7
.2268
37
6.3379
8
6.7777
38
43.2777
8
.2963
38
6.6851
9
6.6260
39
44.9583
9
.3760
39
7.0416
10
7.6000
40
46.6666
10
.4630
40
7.4074
11
.8.4027
41
48.4027
11
.5602
41
7.7824
12
9.3333
^
60.1666
12
.6667
42
8.1666
13
10.2916
43
51.9583
13
.7824
43
8.6602
14
11.2777
44
53.7777
14
.9074
44
8.9629
16
12.2916
46
55.6250
15
1.0417
46
9.3750
16
13.3333
46
67.5000
16
1.1852
46
9.7962
17
14.4027
47
59.4027
17
1.3379
47
10.2268
18
15.5000
48
61.3333
18
1.5000
48
10.6666
19
16.6260
49
63.2916
19
1.6713
49
11.1157
20
17.7777
60
66.2777
20
1.8518
60
11.6740
21
18.9583
61
67.2916
21
2.0417
61
12.0416
22
20.1666
62
69.3333
22
2.2407
62
12.5186
23
21.4027
53
71.4027
23
2.4491
53
13.0046
24
22.6666
54
73.6000
24
2.6667
54
13.5000
26
23.9583
65
76.6250
26
2.8936
55
14.0046
26
26.2777
56
77.7777
26
3.1296
66
14.5186
27
26.6250
57
79.9583
27
3.3750
67
15.0416
28
28.0000
58
82.1666
,28
3.6296
68
16.6740
29
29.4027
59
84.4027
29
3.8936 69
16.1167
30 130.8333
60
86.6666
30
4.1667 60
16.6666
( cxzsiv. )
BASE 33— SLOPE
1
Add.
i
Add.
1
^
1
Li.<t.
1
.6296
31
36.7467
1
.6062
IT
6.9321
2
1.2962
32
38.5186
2
.0247
32
a3210
3
20000
33
40.3333
3
.0565
33
67222
4
2.7407
34
42.1861
4
.0988
34
7.1358
5
3.5185
35
440740
5
.1543
35
7.6617
e
43333
36
46.0000
6
.2222
36
8.0000
7
51851
37
47.9629
7
.3025
37
8.4506
8
6.OT40
38
40.9629
8
.3951
38
8.9135
9
7.0000
39
52.0000
9
.5000
39
9.3888
10
7.9629
40
540740
10
.6173
40
9.8765
11
8.9629
41
56.1851
11
.7469
41
10.3765
12
10.0000
42
68.3333
12
.8889
42
10.8888
13
11.0740
43
60.6185
13
1.0432
43
11.4135
14
12.1851
44
62.7407
14
1.2099
44
11.9506
15
13.3333
45
65.0000
15
1.3889
46
12.5000
16
145185
46
67.2962
16
1.5802
46
13.0617
17
15.7407
47
69.6296
17
1.7839
47
13.6358
18
17.0000
48
720000
18
2.0000
48
14.2222
19
18.2962
49
74.4074
19
2.2284
49
14.8209
20
19.6296
50
76.8518
20
2.4691
50
16.4321
21
21.0000
51
79.3333
21
2.7222
51
16.0.')55
22
22.4074
52
81.8518
22
2.9876
52
16.6913
23
23.8618
63
84.4074
23
3.2654
63
17.3395
24
25.3333
54
87.0000
24
3.5555
64
18.0000
2S
26.8518
55
89.6296
26
3.8530
65
18.6728
26
28.4674
56
92.2962
26
4.1728
56
19.3580
27
30.0000
57
96.0000
27
4.6000
57
20.0555
28
31.6296
68
97.7407
28
4.8395
68
20.7654
29
33.2962
59
100.6186
29
6.1913
69
21.4876
30
36.0000
60
103.3333
30
6.5556
60
22.2222
( CXXXT. )
BASE 33— SLOPE IJ to 1.
1'
•a
Add.
1
Add.
".a
Dedact.
if. of
Hts.
Deduct.
1
s
o
«
.6342
31
41.1898
1
.0077
31
7.4161
]
2
1.3148
32
43.2692
2
.0309
32
7.9012
3
2.0417
33
45.3760
3
.0694
33
8.4027
'^.
4
2.8148
34
47.6370
4
.1234
34
8.9197
1'
).
5
3.6342
35
49.7453
6
.1928
35
9.4521
Oi^
6
4.5000
36
62.0000
6
.2778
36
10.0000
i
7
5.4120
37
54.3009
7
.3781
37
10.6632
)»
8
6.3703
38
66.6481
8
.4938
38
11.1419
3S
9
7.3760
39
69.0417
9
.6260
39
11.7361
10
8.4258
40
61.4814
10
.7716
40
12.3456
Si
11
9.6231
41
63.9676
11
.9336
41
12.9706
12
10.6666
42
66.6000
12
1.1111
42
13.6111
13
11.8664
43
69.0786
13
1.3040
43
142680
If
14
13.0926
44
71.7037
14
1.5123
44
149382
16
14.3760
45
74.3750
15
1.7361
45
15.6260
16
15.7037
46
77.0926
16
1.9753
46
16.3271
17
17.0786
47
79.8664
17
2.2299
47
17.0447
18
18.5000
48
82.6666
18
2.5000
48
17.7777
19
19.9676
49
85.6231
19
2.7866
49
18.5262
20
21.4814
60
88.4258
20
3.0864
60
19.2901
m
0.
21
23.0417
51
91.3750
21
3.4028
51
20.0694
22
24.6481
52
94.3703
22
3.7346
62
20.8641
23
26.3009
53
97.4120
23
4.0818
53
21.6743
24
28.0000
54
100.6000
24
4.4444
64
22.6000
25
29.7453
55
103.6342
25
4.8228
56
23.3410
>
26
31.6370
66
106.8148
26
5.2160
66
24.1975
27
33.3750
57
110.0417
27
6.6260
67
25.0694
28
35.2592
68
113.3148
28
6.0494
68
26.9567
29
37.1898
59
116.6342
29
6.4891
59
26.8596
30
39.1666
60
120.0000
30
6.9444
60
27.7777
( MXXVi. )
BASE 33-SLOPE
IJ to 1.
1
Add.
I
Add.
l^
Dedact.
¥
Dedact.
1
.6388
31
45.6388
1
.0092
31
8.8981
2
1.3333
32
48.0000
2
.0370
32
9.4816
3
20833
33
.50.4166
3
.0833
33
10.0833
4
2,8888
34
62.8888
4
.1480
34
10.7037
5
3.7500
36
55.4166
5
.2313
35
11.3425
6
4.6666
36
58.0000
6
.33.33
36
120000
7
5.6388
37
60.6388
7
.4537
37
126769
8
6.6666
38
63.3333
8
.5926
38
13.3703
9
7.7500
39
06.0833
9
.7500
39
14.0833
10
40
68.8888
10
.9259
40
14.8148
11
10.0833
41
71.7500
11
1.1203
41
15.5648
12
11.3333
42
74.6666
12
1.3333
42
163333
13
126388
43
77.6388
13
1.5648
43
17.1202
14
14.0000
44
806666
14
1.8148
44
17.9259
15
15.4166
45
83.7500
15
20833
45
18.7500
16
16.8888
46
86.8888
16
23704
46
19.6925
17
18.4166
47
90.0833
17
26759
47
20.4537
18
200000
48
93.3333
18
3.0000
48
21.3333
19
21.6388
49
96.6M
19
3.3426
49
22.2314
20
23.3333
50
100.0000
20
3.7037
50
23.1481
21
25.0833
51
103.4166
21
4.0833
51
24.0833
22
26.8888
52
106.8888
22
4.4815
52
25.0370
23
28.7500
53
1104166
23
4.8981
63
26.0092
24
30.6666
54
114.0000
24
5.3333
64
27.0000
25
326388
55
117.6388
26
5.7869
65
28.0092
26
34.6666
56
121.3333
26
6.2592
66
29.0370
27
36.7500
67
125.0833
27
6.7600
67
30.0833
3-1.8888
58
128.8888
28
7.2592
58
31.1481
41.0833
59
132.7500
29
7.7869
59
32.2314
43.3833
60
136.6866
30
8.3333
60
33.3333
( cxxxvii. )
BASE 33— SLOPE If to 1.
Add.
Add.
if. of
Hts.
Deduct.
if. of
Hts.
Dedu<A.
B
X
P
o
1
.6435
31
60.0879
1
.0108
31
10.3811
2
1.3518
32
52.7407
2
.0432
32
11.0617
3
2.1260
33
56.4583
3
.0972
33
11.7638
4
2.9629
34
58.2407
4
.1728
34
12.4876
5
3.8657
36
61,0879
6
.2700
35
13.2330
6
4.8333
36
64.0000
6
.3889
36
14.0000
7
6.8657
37
66.9768
7
.5293
37
14.7885 ■
8
6.9629
38
70.0186
8
.6913
38
15.5987 1
9
8.1250
99
73.1260
9
.8760
39.
16.4305 1
10
9.3518
40
76.2962
10
1.0802
40
17.2839
11
10.6435
41
79.6324
11
1.3071
41
18.1589
12
12.0000
42
82.8333
12
1.6555
42
19.0566
13
13.4214
43
86.1991
13
1.8256
43
19.9747
14
14.9074
44
89.6296
14
2.1173
44
20.9136
16
16.4583
45
93.1250
15
2.4305
45
21.8750
16
18.0740
46
96.6851
16
2.7654
46
^.8580
17
19.7546
47
100.3101
17
3.1219
47
23.8626
18
21.5000
48
104.0000
18
3.5000
48
24.8888
19
23.3101
49
107.7546
19
3.8997
49
25.9367
20
25.1851
60
111.6740
20
4.3210
60
27.0061
21
27.1250
61
115.4683
21
4.7639
61
28.0972
22
29.1296
62
119.4074
22
5.2284
62
29.2098
23
31.1991
63
123.4214
23
5.7145
63
3a3441
24
33.3333
54
127.6000
24
6.2222
64,
31.5000 '■
25
36.5324
55
131.6436
26
6.7516
55
32.6774 !
26
37.7962
66
136.8518
26
7.3024
56
33.8765
27
40.1250
57
140.1260
27
7.8750
57
35.0972
28
42.5185
68
144.4629
28
8.4691
68
36.3394
29
44.9768
59
148.8667
29
9.0848
59
37.6033
30
47.5000 60 153.3333]
30
9.7222
60 38.8888 ■■.
T
( cxxxviii. )
BASE 33-8LOPE 2 to 1.
■
}
X
Add.
1
Add.
a*
Dedact.
saai
O
31
Deduct.
1
.6481
31
546370
1
.0123
11.8642
2
1.3708
32
67.4814
2
.0494
32
12.6419
3
2.1666
33
60.6000
3
.1111
33
13.4444
4
3.0370
34
63.6926
4
.1976
34
14.2716
5
3.9814
36
66.7692
5
.3086
36
15.1234
6
6.0000
36
70.0000
6
.4444
36
16.0000
7
6.0926
37
73.3148
7
.6049
37
lft9012
8
7.2592
38
76.7037
8
.7901
38
17.8271
9
8.6000
39
80.1666
9
1.0000
39
18.7777
10
9.8148
40
83.7037
10
1.2346
40
19.7530
H
11.2037
41
87.3148
11
1.4938
41
20.7530
12
12.6666
42
91.0000
12
1.7778
42
21.7777
13
14.2037
43
94.7592
13
2.0864
43
22.8271
14
16.8148
44
98.6926
14
2.4197
44
23.9012
16
17.6000
46
102.6000
16
2.7778
46
26.0000
16
19.2592
46
106.4814
16
3.1605
46
26.1234
17
21.0926
47
110.6370
17
3.6679
47
27.2716
18
23.0000
48
114.6666
18
4.0000
48
28.4444
19
24.9814
49
118.9703
19
4.4668
49
29.6420
20
27.0370
50
123.1481
20
4.9382
60
30.86^
21
29.1666
61
127.5000
21
6.4444
61
32.1111
22
31.3703
62
131.9269
22
5.9753
62
33.3827
23
33.6481
63
136.4259
23
6.5309
63
34.6790
24
36.0000
64
141.0000
24
7.1111
64
36.0000
25
38.4269
66
145.6481
26
7.7160
65
37.3466
26
40.9269
66
150.3703
26
8.3467
56
38.7160
27
43.6000
57
166.1666
27
9.0000
67
40.1111
28
46.1481
68
160.0370
28
9.6790
58
41.6308
29
48.8703
69
164.9814
29
10.3827
69
42.9763
30
61.6666
60
170.0000
30
11.1111
60
44.4444
( cxxxix. )
BASE 33— SLOPE 2i to 1.
■a
'S
s
1
Add.
1
s
Add.
Dif.of
Hte.
Deduct,
Dif,of
Hts,
Dedoct
,6674
31
63.4352
1
,0164
31
14,8302
2
1.4074
32
66.9629
2
,0617
32
16,8013
3
2.2500
33
70.5833
3
.1389
S3
16.8065
4
3.1852
34
74.2963
4
.2468
34
17,8396
5
4.2129
35
78.1018
5
,3857
36
18.9043
6
5.3333
36
82,0000
6
,5666
36
20,0000
7
&5463
37
86.9907
7'
,7561
37
21,1266
8
7.8518
38
90.0740
8
,9876
38
22.2839
9
9.2500
39
94.2600
9
1,2500
39
23,4722
10
10.7407
40
98,6186
10
1,6432
40
24.6913
11
12.3241
41
102.8796
11
1.8673
41
25,9413
12
14.0000
42
107,3333
12
2,2222
42
27^2222
13
15.7685
43
111.8796
13
2,6080
43
2a5360
14
17.6296
44
116.6185
14
3.0247
44
29.8765
15
19.5833
46
121,2600
15
3,47^
45
31.2600
16
21.6296
46
126.0740
16
3.9606
46
32.6543
17
24.7685
47
130.9907
17
4.4599
47
34,0895
18
26.0000
48
136.0000
18
6,0000
48
36.6665
19
28.3241
49
141,1018
19
5,5710
49
37,0524
20
30.7407
50
146.2963
20
&1728
50
38.5802
21
33.2600
51
151,5833
21
6.8056
51
40.1388
22
35.8518
62
156.9629
22
7.4691
62
41,7283
23
38.5463
53
162,4362
23
8.1636
63
43.3487
24
41.3333
54
168.0000
24
8.8889
64
45.0000
25
44.2129
65
173.6574
25
9.6466
65
46,6820
26
47.1852
56
179.4074
26
10.4321
66
48,3960
27
50.2600
67
185.2600
27
11.2500
67
60,1388
28
53.4074
58
191.1862
28
12,0587
58
51,9135
29
56.6674
59
197,2129
29
12.9782
69
53,7191
30
60.0000
60
203.3333
30
13,8889
60
66.5656
( cxl. )
BASE 33— SLOPE 3 to 1.
»
1
2
3
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
26
26
27
28
29
30
Add.
.6666
1.4444
2.3333
3.3333
4.4444
5.6666
7.0000
8.4444
10.0000
11.6666
13.4444
15.3333
17.3333
19.4444
21.6666
24.0000
27.4444
29.0000
31.6666
34.4444
37.3333
40.3333
43.4444
46.6666
50.0000
53.4444
57.0000
60.6666
64.4444
68.3333
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
^
56
57
58
59
60
Add.
72.3333
76.4444
80.6666
85.0000
89.4444
94,0000
98.6666
103.4444
108.3333
113.3333
118.4444
123.6666
129.0000
134.4444
140.0000
145.6666
151.4444
157.3333
163.3333
169.4444
175.6666
182.0000
188.4444
195.0000
201.6666
208.4444
215.3333
222.3333
229.4444
236.6666
Q
1
2
3
4
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Deduct.
.0185
.0740
.1667
.2963
.4628
.6667
.9074
1.1852
1.5000
1.8518
2.2407
2.6667
3.1296
3.6296
4.1667
4.7407
5.3518
6.0000
6.6852
7.4074
8.1667
8.9629
9.7962
10.6667
11.5741
12.5184
13.5000
14.5185
15.5741
16.6667
Deduct.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60 66.6666
17.7963
18.9630
20.1666
21.4074
22.6851
24.0000
25.3518
26.7407
28.1666
29.6296
31.1296
32.6666
34i2407
35.8518
37.5000
39.1851
40.9074
42.6666
44.4629
46.2963
49.1666
50.0740
52.0185
54.0000
56.0184
58.0740
60.1666
62.2962
64.4629
d
i
1
1
1
( cxli. )
BASE 34— SLOPE J to 1.
s
K
1
Add.
1
SB
Add.
1
Deduct.
a"
81
Deduct.
.6342
31
23.9676
.0015
1.4830
2
1.2777
32
24.8888
2
.0062
32
1.5802
3
1.9305
33
25.8194
8
.0139
38
1.6805
4
2.5926
34
26.7592
4
.0246
84
1.7839
5
3.2638
35
27.7083
5
.0386
85
1.8904
6
3.9444
36
28.6666
6
.0655
86
2.0000
7
4.63^
37
29.6342
7
.0756
37
2.1126
8
5.3333
38
30.6111
8
.0988
38
2.2284
9
6.0416
39
31.5972
9
.1260
89
2.3472
10
6.7592
40
32.5926
10
.1643
40
2.4691
11
7.4861
41
83.5972
11
.1867
41
2.5941
12
8.2222
42
346111
12
.2222
42
2.7222
13
8.9676
43
36.6342
13
.2608
48
2.8645
14
9.7222
44
36.6666
14
.3025
44
2.9876
16
10.4861
45
37.7083
15
.3472
46
8.1250
16
11.2592
46
38.7592
16
.8951
46
8.2664
17
12.0416
47
39.8194
17
.4460
47
3.4089
18
12.8333
48
40.8888
18
.6000
48
3.6665
19
13.6342
49
41.9676
19
.6571
49
8.7052
20
14.4444
50
43.0565
20
.6178
50
3.8580
21
15.2638
51
44.1527
21
.6805
61
4.0139
22
160926
62
45.2592
22
.7469
52
4.1728
23
16.9305
53
46.3750
23
.8168
63
4.8349
24
17.7777
64
47.5000
24
.8889
64
4.6000
25
18.6342
55
48.6342
26
.9647
55
4.6682
26
19.5000
66
49.7777
26
1.0482
56
4.8396
27
2a3760
57
60.9305
27
1.1260
57
5.0139
28
21.2592
58
62.0926
28
1.2099
58
5.1913
29
22.1527
69
53.2688
29
1.2978
59
6.3719
1 30
23.0555
60
64.4444
30
1.3889 60
6.6665
( cxlii. )
BASE 34— SLOPE J to 1.
1
Add.
«2 Height
1
.6388
2
1.2962
32
a
1.9722
33
4
2.6666
34
5
3.3796
35
6
41111
36
7
4.8611
37
8
5.6296
38
9
6.4166
39
10
7.2222
40
11
8.0462
41
12
8.8888
42
13
9.7500
43
14
10.6296
44
15
11.6277
45
16
12.4444
46
17
13.3796
47
18
14.3333
48
19
15.3055
49
20
16.2962
50
21
17.3055
51
22
18.3333
52
23
19.3796
53
24
20.4444
54
25
21.5277
55
26
22.6296
56
27
23.7500
57
28
24.8888
58
29 26.0462
59
30
27.2222
60
Add.
28.4166
29.6296
30.8611
32.1111
33.3796
34.6666
35.9722
37.2962
38.6388
40.0000
41.3796
42.7777
44.1944
45.6296
47.0833
48.5555
50.0462
51.5555
53.0833
54.6296
56.1944
57.7777
59.3796
61.0000
62.6388
64.2962
65.9722
67.6666
69.3796
71.1111
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Deduct.
.0031
.0123
.0278
.0494
.0772
.1111
.1512
.1975
.2500
.3734
.4444
.5216
.6049
.6944
.7901
.8920
1.0000
1.1142
1.2346
1.3611
1.4938
1.6327
1.7778
1.9295
26 2.0864
27
28
29
30
•2.2500
2.4197
2.5956
2.7778
i^
Deduct.
31
32
33
34
35
96
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
56
56
57
58
59
60
2.9660
3.1605
3 3611
3.5679
3.7808
4.0000
4.2*253
4.4568
4.6944
4.9383
5.1883
5.4444
5.7067
5.9753
6.2500
6.5308
6.8179
7.1111
7.4105
7.7160
8.0277
8.3456
8.6697
9.0000
9.3364
9.6790
10.0277
10.3827
10.7438
11.1111
( cxliii. )
BASE 34 SLOPE | to 1. \
1
Add.
•4>>
31
Add.
tea)
a
1
Deduct.
Dif. of
Hts.
1
Deduct.
1
.6435
32.8657
.0046
31
4.4490
1
2
1.3148
32
34.3703
2
.0185
32
4.7407
3
2.0138
33
36.9027
3
.0416
33
5.0416
4
2.7407
34
37.4629
4
.0740
34
6.3518
5
3.4953
35
39.0609
6
.1157
35
5.6712
6
4.2777
36
40.6666
6
.1667
36
6.0000
7
5.0879
37
42.3101
7
.2268
37
6.3379
8
5.9259
38
43.9814
8
.2963
38
6.6851
9
6.7916
39
45.6805
9
.3750
39
7.0416
10
7.6851
40
47.4074
10
.4630
40
7.4074
11
8.6044
41
49.1620
11
.5602
41
7.7824
12
a5565
42
50.9444
12
.6667
42
8.1666
13
10.5324
43
52.7546
13
.7824
43
8.5602
14
11.5370
44
64.5926
14
.9074
44
8.9629
15
12.5694
45
56.4583
16
1.0417
45
9.3750
16
13.6296
46
58.3618
16
1.1862
46
&.7962
17
14.7176
47
60.2731
17
1.3379
47
10.2268
18
16.8333
48
62.2222
18
1.5000
48
10.6666
19
16.9768
49
64.1990
19
1.6713
49
11.1157
20
18.1481
60
66.2087
20
1.8618
60
11.5740
21
19.5694
51
68.2361
21
2.0417
61
12.0416
22
20.5740
52
70.2962
22
2.2407
52
12.5185
23
21.8287
53
72.3842
23
2.4491
53
13.0046
24
23,1111
54
74.5000
24
2.6667
54
13.5000
25
24.4214
65
76.6435
25
28935
65
14.0046
26
25.7037
56
78.8148
26
3.1296
56
14.5185
27
27.1250
57
81.0138
27
3.3760
57
15.0416
28
28.6185
68
83.2407
28
3.6296
58
15.5740
29
29.9398
59
85.4953
29
3.8936
59
16.1157
30
31.3888
60
87.7777
30
4.1667
60
16.6666
( cxliv. )
BASE 34^8LOPE 1 to 1.
1
Add.
1
Add.
I
Dednct.
Deduct,
1
.6481
31
37.8148
.0062
31
6.9321
2
1.3333
32
39.1111
2
.0247
32
a321«
3
2.0555
33
40.9444
3
.0555
33
6.7222
4
2.8148
34
42.8148
4
.0988
34
7.1358
5
3.6111
35
447222
6
.1543
36
7.5617
6
4.4444
36
46.6666
6
.2222
36
8.0000
7
5.3148
37
48.6481
7
.3026
37
8.4506
8
6.2222
38
50.6666
8
.395 L
38
8.9136
9
7.1666
39
52.7222
9
.5000
39
9.3888
10
8.1481
40
54.8148
10
.6173
40
9.8766
11
9.1666
41
56.9444
11
.7469
41
10.3765
12
10.2222
42
59.1111
12
.8889
42
10.8888
13
11.3148
43
61,3148
13
1.0432
43
11.4136
14
12.4444
44
63.6565
14
1.2099
44
11.9506
15
13.6111
46
65.8333
16
1.3889
45
12.6000
16
14.8148
46
68.1481
16
1.6802
46
13.0617
17
16.0556
47
70.5000
17
1.7839
47
13.6358
18
17.3333
48
72.8888
18
2.0000
48
14.2222
19
18.6481
49
75.3148
19
2.2284
49
14.8-209
20
20.0000
50
77.7777
20
2.4691
50
16.4321
21
21.3888
61
80.2777
21
2.7222
51
ia0555
22
22.8148
52
82.8148
22
2.9876
52
16.6913
23
24.2777
63
86.3888
23
3.2654
53
17.3395
24
26.7777
54
88.0000
24
3.5556
64
18.0000
26
27.3148
65
90.6481
26
3.8580
55
18.6728
26
28.8888
56
93.3333
26
4.1728
56
19.3580
27
30.6000
57
96.0555
27
4.5000
57
20.0555
28
32.1481
58
98.8148
28
4.8395
68
20.7664
29
33.8333
59
101.6111
29
6.1913
69
21.4876
30
36.5565 60
104.4444
30
5.5566
60
22.2222
( cxlv. )
BASE 34— SLOPE 1^ to 1.
•**
•r
1
Add.
1
Add.
1
Dedaot.
s
Deduct.
.6527
81
41.7639
.0077
31
7.4161
2
1.3518
32
43.8618
2
.0309
32
7.9012
8
2.0972
38
45.9861
8
.0694.
38
8.4027
4
2.8888
84
48.1666
4
.1234
34
8.9197
5
3.7268
86
60.3935
6
.1928
36
9.4621
6
4.6111
86
62.6666
6
.2778
36
10.0000
7
6.5416
37
64.9861
7
.3781
87
10.5632
8
&5186
38
57.8518
«
.^S38
38
11.1419
9
7.6416
39
59.7639
9
.6260
39
11.7861
10
8.6111
40
62.2222
10
.7716
40
12.8466
11
9.7266
41
64.7268
11
.9838
41
12.9706
12
ia8888
^
67.2777
12
LllU
42
18.6111
13
12.0972
48
69.8760
IS
1.3040
48
14.2680
14
18.3618
44
72.5186
14
1.6128
44
14.9882
16
14.6627
45
76.2088
16
1.7361
45
16w62d0
16
IftOOOO
46
77.9444
16
1.9768
46
16.3271
17
17.3936
47
8a7268
17
2.2290
47
17.0447
18
18.8333
48
83.6656
18
2.5000
48
17.7777
19
20.3194
49
8a4306
19
2.7865
49
18.6262
20
21.8618
69
89.3618
20
a0864
60
19.2901
21
28.4306
61
92.8194
21
8.4028
61
20.0694
22
25.0555
62
95.3338
22
3.7846
62
20.8641
28
26.7268
68
98.3985
23
4.0818
63
21.6743
24
28.4444
64
101.5000
24
4.4444
64
22.6000
25
80.2083.
65
104.6627
26
4.8228
66
aa34io
26
32.0186
66
107.8618
26
6.2160
66
24.1976
27
3a8750
67
111.0972
27
6.6260
67
26.C694
28
36.7777
68
114.3888
28
6.0494
68
26.9567
29
87.7268
69
117.7268
29
6.4891
50
26^596
30
3a7222
60
12L1111
30
6.9444
60
V
27.7777
'i
(oxlvi. )
BASE 32— SLOPE 1^ to 1.
}
Add.
n
Add.
1
Dednct.
I>if.of
Deduct.
1
.6574
31
46.2129
.0092
31
8.8981
2
1.8708
82
48.6926
2
.0370
32
9.4815
3
2.1388
33
61.0277
8
.0633
83
10.0833
4
2.9629
34
53.6186
4
.1480
34
10.7087
6
8.8426
35
66.0648
5
.2318
85
11.3435
6
4.7777
86
68.6666
6
.3833
86
12.0000
7
5.7685
37
61.8240
7
.4537
37
12.6769
8
a8148
38
64.0370
8
.5926
38
18.3703
9
7.9166
89
66.8065
9
.7500
89
14.0838
10
9.0740
40
69.6296
10
.9259
40
148148
U
10.2870
41
72.6092
11
1.1208
41
15.6648
12
11.5555
42
75.4444
12
1.3333
4a
16.3338
13
12.8796
48
78.4861
13
1.5648
48
17.1202
14
14.2592
44
81.4816
14
1.8148
44
17.9259
lis
15.6944
45
84US833
15
2.0883
46
18.7600
16
17.1851
46
87.7407
16
2.3704
46
19.6926
17
18.7316
47
90.9637
17
2.6769
47
20.4637
18
20.3333
48
18
3.0000
48
21.8333
19
21.9907
49
97.6463
19
3.3426
^
22.2314
20
23.7037
50
100.9259
20
3.7037
50
23.1481
21
25.4722
51
104.8611
21
4.0833
51
24.0838
22
27.2963
52
107.8518
22
4.4816
52
26.0370
23
29.1760
53
111.3981
23
4.8981
58
26.0092
24
31.1111
54
115.0000
24
6.3333
54
27.0000
25
33.1018
55
118.6574
25
6.7869
55
28.0092
26
35.1481
56
122.8703
26
6.2692
56
29.0370
27
37.2500
57
126.1388
27
6.7500
57
30.0838
28
39.4074
58
129.9629
28
7.2692
68
31.1481
29
41.6203
59
183.8^6
29
7.7869
59
32.2314
30
48.8888
60
137,7777
90
8.3833
60
3.38388
L
( cxlvii. )
BASE 34— SLOPE 1} to 1.
%.
S
■s--
"8.-
•r
a
1
Add.
a
Add.
gS
Dednot.
gl
Dednet.
.6620
31
50.6620
1
.0106
81
10.3811
2
1.3888
32
53.3333
2
.0432
32
11.0617
3
2.1805
33
56.0694
3
.0972
38
11,7638
4
3.0370
34
58.8703
4
.1728
34
12.4876
6
3.9583
35
61.7361
5
.2700
35
13.2380
6
4.9444
36
64.6666
6
.3889
36
14.0000
7
5.9963
37
67.6620
7
.5293
87
14.7885
8
7.1111
38
70.7222
8
.6913
38
15.6987
9
8.2916
39
73.8472
9
.8760
89
16.4305
10
9.5370
40
77.0370
10
1.0802
40
17.2839
11
10.8472
41
80.2916
11
1.3071
41
18.1689
12
12.2222
42
83.6111
12
1.5665
4&
19.0665
13
13.6620
43
86.9953
13
1.8266
43
19.9747 :
14
15.1666
44
90.4444
14
2.1173
44
20.9135 '
15
16.7361
45
93.9583
15
2.4305
45
21.8750 1
16
18.3703
46
97.5370
16
2.7654
46
22.a'i80
17
20.0694
47
101.1806
17
3.1219
47
23.8626
18
21.8333
48
104.8888
18
3.5000
48
24.8888
19
23.6620
4Q
108.6620
19
3.8997
49
25.9367
20
25.5555
50
112.5000
20
4.3210
50
27.0P61
21
27i>138
51
116.4027
21
4.7639
51
28.0972
22
29.5370
52
120.3703
22
5.2284
52
29.2098
28
31.6250
53
124.4027
23
5.7145
53
30.3441
24
33.7777
54
128.600J
24
8.2228
54
31.5000
25
35.9953
56
132.6620
25
6.7616
55
32.6774
26
38.2777
66
136.8888
26
7.3024
56
88.8765
27
40.6250
57
141.1805
27
7.8760
57
35.0972
28
43.0370
58
146.5870
28
8.4691
58
36.8394
29
45.5188
59
149.9583
29
9.0848
59
37.6033
80
48.0555 60
154.4444 1 30
».7222
60
OOaOOOO
( czlviii. )
BASE 34-8LOP£ 2 to 1.
1
1
Add.
1
n
31
Add.
a"
1
Deduct.
Deduct.
•QDOO
66.1111
.0123
31
11.8642
2
1.4074
32
68.0740
2
.0^4
32
12.6419
S
2.2222
88
61.1111
3
.1111
33
18.4444
4
3.1111
84
64.2222
4
.1975
84
142716
d
4.0740
36
67.4074
6
.3086
35
16.1284
6
5.1111
86
70.6866
6
.4444
36
laoooo
7
6.2222
37
74.0000
7
.60^
37
16.9012
8
7.4074
88
77.4074
8
.7901
38
17.8271
9
8.6666
39
80.8888
9
1.0000
39
18.7777
10
10.0000
40
844444
10
1.2346
40
I9.75S0
11
11.4074
41
88.0740
11
1.4938
41
20.7530
12
12.8888
42
91.7777
12
1.7778
42
21.7777
13
144444
48
95.5555
13
2.0664
48
22.8271
14
16.0740
44
99.4074
14
2.4197
44
23.9012
15
17.7777
45
108.8883
15
2.7778
45
25.0000
16
19.5556
46
107.3883
16
3.1605
46
S8.1234
17
21.4074
47
111.4074
17
8.5679
47
27.2716
18
23.8833
48
115.6655
18
40000
48
28.4444
19
25.3833
49
119.7777
19
4.4568
49
29.6420
20
27.4074
60
124.0740
20
49882
50
8a86^
21
29.5555
61
129.4444
21
6.4444
61
82.1111
22
31.7777
52
132.8888
22
5.9753
62
83.3827
23
34.0740
58
137.4074
23
6.6309
53
84.67fl0
24
36.4444
64
142.0000
24
7.1111
64
36.0000
25
38.8888
56
146.6666
$25
7.7160
65
87.8456
26
41.4074
66
151.4074
26
8.8467
66
88.7160
27
44.0000
67
166i2222
27
9.0000
57
40J111
28
46.6666
58
161J111
28
9.6790
68
41i>808
29
49.4074
59
166.0740
29
10.8827
69
42.9753
90
52.2222160
171.1111
SO
11.1111 ' 60
44.4444
( cxlix. )
BASE 34— SLOPE 2^ to 1,
1
Add.
1
a
Add.
Dif.of
Hte.
•
DedMt
Dif.or
Hte.
Dednct.
1
.6759
31
640092
1
J0154
81
148802
2
1.4444
32
67.5555
2
.0617
82
15.8015
3
2.3055
33
71.1944
3
.1389
33
16.8066
4
3.2592
34
749269
4
.2468
34
17.8896
5
43055
35
78.7500
5
.3857
85
18.9043
6
5.4444
36
82.6666
6
.5665
36
20.0000
7
6.6759
37
86.675»
7
.7661
37
21.1266
8
8.0000
38
90.7777
8
.9876
38
22.2839
9
9.4166
39
94.9722
9
1.2500
39
23.4722
10
10.9260
40
9d.2Sd2
10
1.5432
40
246913
11
12.6277
41
103.6388
11
1.8673
41
26.9413
12
14.2222
42
108.1111
12
2.2222
42
27.2222
13
ia0092
43
112.6759
13
2.6080
43
28.5860
14
17.8888
44
117.3333
14
3.0247
44
29.8765
15
19.8611
45
122.0833
16
3.4722
45
31.2600
16
■21.9259
46
126;9259
16
3.9506
46
32.6643
17
24.0833
47
131.8611
17
44699
47
34.0895
18
26.3333
48
136.8888
18
5.0000
48
36.5666
19
28.6759
49
142.0092
19
6.6710
49
37.0524
20
31.1111
50
147.2222
20
6.1728
60
88.6802
21
34.6388
51
152.5277
21
6.8055
61
40.1388
22
36.2592
52
157.9259
22
7.4601
62
41.7283
23
38.9722
53
163.4166
23
8.1636
53
43.3487 ,
24
41.7777
54
169.0000
24
8.8889
64
46.0000
25
45.6759
55
174.6759
25
9.6455
65
46.6820
26
47.6666
56
180.4444
26
10.4321
56
48.3950
27
50.7500
57
186.3055
27
11.2500
57
50.1388
28
53.9259
58
192.2592
28
12.0587
68
61.9135
29
57.1944
59
198.3055
29
12.9782
69
53.7191
30 60.5555
1
60
204.4444
30 13.8889
60
55.6565
(d.)
BASE 84— SLOPE 3 to 1.
1
Add.
1
n
Add.
Deduct.
Deduct.
1
.6851
31
72.9074
1
.0185
31
17.7963
2
1.4814
32
77.0370
2
.0740
32
18.9630
3
2.3888
33
81.2777
8
.1667
83
20.1666
4
3.4074
34
85.6296
4
, .2963
34
21.4074
6
4.5370
35
90.0926
5
.4628
86
22.6851
6
5.7777
36
946666
6
.6667
36
240000
7
7.1296
37
99.3618
7
.9074
87
26.3618
8
8.5925
38
104.1481
8
1.1862
38
26.7407
9
10.1666
39
109.0555
9
1.5000
39
28.1666
10
11.8518
40
1140740
10
1.8518
40
29.6296
11
13.6481
41
119.2037
11
2.2407
41
81.1296
12
15.5555
42
124.4444
12
2.6667
42
82.6666
13
17.5740
43
129.7962
13
3.1296
48
34.2407
14
19.7037
44
136.2692
14
3.6296
44
35.8518
16
21.9444
45
140.8333
16
41667
46
37.5000
16
24.2962
46
146.6186
16
47407
46
39.1861
17
26.7692
47
152.8148
17
5.8618
47
40.9078
18
29.3333
48
158.2222
18
aoooo
48
42.6666
. 19
32.0185
49
164.2407
19
6.6862
49
444^29
20
34.8148
50
170,3708
20
7.4074
50
46.2963
21
37.7222
61
176.6111
21
8.1667
51
49.1666
22
40.7407
52
182.9629
22
8.9629
52
60,0740
23
43.8703
53
189.4259
23
9.7962
63
62.0185
24
47.1111
54
196.0000
24
10.6667
64
64.0000
25
50.4^9
56
202.6861
26
11.6741
55
6a0184
26
58.9259
66
209.4814
26
12.5184
66
58.0740
27
57.6000
67
216.3888
27
13.6000
67
60.1666
28
61.1861
68
223.4074
28
146185
68
62.2962
29
64.9814
69
230.6370
29
15.5741
59
64.4629
30
Do«oooo
60
237.7777
30
lft6667
60 66.6666
( cM. )
BASE 35-SLOPi
: i to 1.
Hdig^t
Add.
1
n
Add.
li
9B
Dedoet
Dednct.
1
.6527
31
245416
1
.0015
31
1.4880 !
2
1.3148
32
25.4814
2
.0062
32
1.5802
3
1.9861
33
26.4305
3
.0189
83
1.6806
4
2.6666
34
27.3888
4
.0246
34
1.7889
6
3.3564
35
28.3564
5
.0885
85
1.8904
6
4.0555
36
29.3333
6
.0555
36
2.0000
7
4.7638
37
30.8194
7
.0756
37
2.1126
8
5.4814
38
31.3148
8
.0968
38
2.2284
9
6.2083
39
32.8194
9
.1250
30
2.3472
10
&9444
40
33.3383
10
.1548
40
2.4691
11
7.6898
41
34.3564
11
.1867
41
2.6041
12
8.4444
4a
35.3888
12
.2222
42
2.7222
13
9.2083
43
36.4305
13
.2608
43
2.8546
14
9.9814
44
37.4814
14
.3026
44
2.9876
15
10.7638
45
88.5416
15
.3472
45
8.1250
16
11.6555
46
89.6111
16
.3961
46
3.2664
17
12.3564
47
40.6898
17
.4460
47
8.4089
18
13.1666
48
41.7777
18
.6000
48
3.5655
19
13.9861
49
42.8750
19
.5571
49
3.7062
20
14.8148
50
48.9814
20
.6173
50
8.8680
21
15.6527
51
45.0972
21
.6805
51
4.0180
22
16.5000
52
46.2222
22
.7469
52
41728
23
17.3564
53
47.3564
23
.8163
68
48840
24
18.2222
54
48.5000
24
.8889
54
46000 :
25
19.0972
55
^.6527
25
.9647
55
46682
26
19.9814
56
50.8148
26
1.0432
66
48305
27
20.8750
57
51.9861
27
1.1250
67
6.0189
28
21.7777
58
53.1666
28
1.2099
58
6.1913
29
22.6898
59
54.3564
29
1.2978
59
6.8719
30
23.6111
60
55.5555
30
1.3889
60
5.5566
( clii. )
BASE 36— SLOPE | to 1.
1
Add.
1
Add.
Dif.of
Htf.
Dednot
Dif.of
Uts.
Deduct
1
.6674
81
28.9907
1
.0031
31
2.9660
2
1.3338
82
30.2222
2
.0123
32
3.1605
8
2.0277
88
31.4722
3
.0278
38
3.3611
4
2.7407
84
32.7407
4
.0494
84
a6679
6
3.4722
85
34.0277
6
.0772
35
a7808
6
42222
86
36.3833
6
.1111
36
40000
7
49907
87
36.6574
7
.1512
37
42253
8
6.7777
88
38.0000
8
.1976
38
44668
9
&d888
89
39.3611
9
.2500
89
46944
10
7.4074
40
40.7407
10
.3086
40
49383
11
8.2500
41
42.1388
11
.3734
41
5.1883
12
9.1111
42
43.5666
12
.4444
42
6.4444
13
a9907
43
449907
13
.5216
43
6.7076
14
10.8888
44
.46.4444
14
.6049
44
5.9753
15
11.8066
46
47.9166
15
.6944
46
J6.2500
16
12.7407
46
4a4074
16
,7901
46
6.5306
17
13.6944
47
60.9166
17
.8920
47
6.8179
18
146666
48
52.4444
18
1.0000
48
7.1111
19
15.6574
49
53.9907
19
1.1143
49
7.4105
20
ia6666
60
66.5655
20
1.2346
60
7.7160
21
17.6944
51
67.1388
21
1.3611
61
8.0277
22
18.7407
52
58.7407
22
1.^38
82
8.3456
23
19.8065
53
60.3611
23
1.6327
63
8.6697
24
20.8888
64
62.0000
24
1.7778
64
9.0000
25
21.9907
56
63.6674
26
1.9296
65
9.3364
26
23.1111
66
65.3333
26
2.0664
66
9.6790
27
242500
57
67.0277
27
2.2500
57
10.0277
28
25.4074
58
68.7407
28
2.4197
68
10.3827
29
26.5888
59
70.4722
29
2.5966
50
10.7438
80
27.7777
60
72.2222
30
2.7778 60 Ill.llU
( diii. )
BASE 35— SLOPE
. f to 1.
Add.
Add.
if. of
Hts.
Deduct.
if. of
Hts.
Deduct.
ta
S3
Q
O
1
.6620
31
33.4396
1
.0046
31
4.4490
2
1.3518
32
34.8518
2
.0186
32
47407
3
2.0694
33
36.6139
3
.0416
83
5.0416
4
2.8148
34
38.0926
4
,0740
34
5.3518
6
3.5879
36
39.6990
6
.1167
36
6.6712
6
4.3888
36
41.3838
6
.1667
36
6.0000
7
6.2176
37
42.9968
7
.2268
87
6.3379
8
6.074IJ
38
44.6851
8
.2963
38
6.6861
9
6.9583
89
46.4027
9
.3760
dd
7.0416
10
7.8708
40
48.1481
10
.4630
40
7.4074
11
8.8102
41
49.9214
11
.5602
41
7.7824
12
9.7777
42
61.7222
12
.6667
42
8.1666
. 13
10.7731
48
63.6509
13
.7824
48
8.6602
14
11.7963
44
55.4074
14
.0074
44
8.9629
16
12.8472
45
67.2916
15
1.0417
45
9.3760
16
13.9269
46
59.2037
16
1.1852
46
9.7962
17
16.0324
47
61.1435
17
1.3379
47
10.2268
18
16.1666
48
63.1111
18
1.5000
48
10.6666
19
17.3287
49
65.1J066
19
1.6713
49
11.1167
ao
18.5186
50
67.1296
20
1.8618
50
11.6740
21
19.7361
61
69.1805
21
2.0417
51
12.0416
22
20.9816
62
71.2892
22
2.2407
52
12.6185
28
22.2546
53
7a3657
23
2.4491
58
18.0046
24
23.5655
54
75.5000
24
2.6667
64
13.6000
25
248842
55
77.6620
25
2.8935
66
140046
26
26.2407
56
79.8618
26
3.1296
66
14.6185
27
27.6260
67
82.0694
27
3.8750
67
16.0416
28
29.0370
68
84.3148
28
3.6296
68
16.5740
29
3a4768
59
86.6879
29
8.8936
59
1&1157
30
•
31.9444
60
88.8888
30
41667
m
X
16.6666
I
( cliv. )
BASE 35 SLOPE 1 to 1. j|
1
Add.
1
Add.
if. of
Btf.
Dednet.
•8^
«JM Deduct.
n
1
m
1
Q
.6666
31
37.8888
.0062
31
6.9321
2
1.3703
32
39.7037
2
.0247
32
6.3210
3
2.1111
33
41.5556
8
.0555
33
6.7222
4
2.8888
34
43.4444
4
.0988
34
7.1368
5
3.7037
85
46.3708
5
.1543
85
7.6617
6
4.5555
36
47.3833
6
86
8.0000
7
6.4444
87
49.3338
7
.8025
87
8.4506
8
6.3703
38
61.8703
8
.8951
88
8.9185 :
9
7.3333
39
63.4444
9
.6000
89
9.3888
10
8.3333
40
55.6555
10
.6173
40
9.8766
11
9.3703
41
57.7037
11
.7469
41
10.3766
12
10.4444
42
59.8888
12
.8889
4a,
10.8888
13
11.6655
43
62.1111
13
1.0432
43
11.4135
14
12.7087
44
64.8703
14
1.2099
44
11.9506
16
13.8888
46
«6.6666
15
1.3889
45
12.6000
16
16.1111
46
69.0000
16
1.5802
46
13.0617
17
16.3703
47
71.8708
17
1.7839
47
18.6358
18
17.6666
48
73.7777
18
2.0000
48
14.2222
19
19.0000
49
76.2222
19
2.2284
49
14.8209
20
20.3703
60
78.7087
20
2.4691
60
16.4321
21
21.7777
51
81.2222
21
2.7222
51
16.a%6
22
23.2222
62
83.7777
22
2.9876
52
16.6913
23
247037
63
86.8708
23
3.2654
53
17.8395
24
26.2222
54
89.0000
24
8.5556
54
18.0000
25
27.7777
66
91.6666
26
3.8680
55
18.6728
26
29.3703
66
94.3708
26
4.175»
56
19.3680
27
31.0000
67
97.1111
27
4.5000
57
20.0555
28
32.6666
68
99.8888
28
4.8395
58
20.7664
29
34.3703
59
102.7037
29
5.1913
■59
21.4876
SO
36.1111
60
105.5565
30
6.5555
60
22.2^2
» *
( cl^. )
BASE 35— SLOPE
IJ to 1.
1
Add.
S
Add.
If. of
Deduct.
3^
1*
Deduct.
#
»
s
31
Q
Q
1
.6712
42.3379
1
.0077
31
7.4161
:
2
1.3888
%2
444444
2
.0309
32
7.9012
3
2.1527
33
4&d972
3
.0694
33
8.4027
4
2.9^9
34
4a79e2
4
.1-234
34
8.9197
5
a8194
35
51.0416
5
.1928
35
9.4S21
>
6
472^
36
53.3333
6
.2778
36
10.0000
•
7
5.6712
37
55.6712
7
.3781
37
10.5632
8
6.6666
38
58.0555
8
.4938
38
11.1419
9
7.7083
39
60.4861
9
.6260
39
11.7361
10
8.7962
40
^9629
10
.7716
40
12.3466
11
9.9305
41
65.4861
11
.9336
41
12.9706
12
11.1111
42
68.0555
12
1.1111
4a
ia6111
13
12.3379
43
70.6712
13
1.3040
43
14268C
14
13.6111
44
73.3333
14
1.5123
44
149382
IS
14.9305
45
7&0416
15
1.7361
45
15.&250
16
1&2962
46
78.7962
16
1.9753
46
16.»271
17
17.7083
47
81.99I7'2
17
2.2299
47
17.0447
18
19.1666
48
84.4444
18
2.5000
48
17.7777
19
20.6712
49
87.3379
19
2.7856
49
18.5262
20
22.2222
50
90.2777
20
3.0864
60
19.2901
21
23.8194
51
93.2638
21
3.4028
51
20.0694
22
25.4629
52
96.2962
22
3.7346
62
20.8641
23
27.1527
53
99.3760
23
4.0818
53
21.6743
'
^
28.8888
54
102.5000
24
4.4444
54
22.5000
26
30.6712
55
105.6712
25
48228
66
23.3410
1
26
32.5000
66
108.8888
26
6.2160
66
24.1975
27
343760
57
112.1627
27
6.6260
57
26.0694
28
36.2962
58
116.4629
28
6.0494
58
26.9667
29
88.2638
59
118.8194
29
6.4891
69
26.8595
1
1
30
40.2777
60
122.2222
30
6.9444
60
27.7777
( dvi. )
BASE 85— SLOPE IJ to 1.
1
Add.
1
Add.
3S
Deduct.'
3^
Dednct.
a
a
o
Q
1
.67d9
31
46.2870
1
.0092
31
8.8961
2
1.4074
32
49.1851
2
.0370
%
9.4816
3
2.1944
33
61.6888-
a
.0633
33
10.0833
4
3.0S70
34
541481
4
.1480
84
10.7037
5
3.9351
35
66,7129
6
.2313
35
11.3425
6
4.8888
36
59.3333
6
.3333
86
12.0000
7
5.8981
37
eojooaa
7
.4537
37
12.6769
8
6.9629
88
647407
8
.6026
88
ia3708
9
8.0833
39
67.5277
9
.7500
39
140838
10
9.2592
40
70.3703
10
.9269
40
148148
11
10.4007
41
7a2685
11
1.1203
41
16.6648
12
11.7777
42
76.2222
12
1.3333
42
16.3333
13
13.1203
43
79.2314
13
1.5648
43
17.1202
14
14.5185
44
82.2962
14
1.8146
44
17.9269
15
15.9722
45
85.4166
16
2.0833
46
18.7500
16
17.4814
46
8a6925
16
2.3704
46
19.6925
17
19.0462
47
91.8240
17
2.6759
47
20.4537
18
20.6666
48
95.1111
18
aoooo
48
21.3333
19
22.3425
49
98.4637
19
3.3426
49
22.2314
20
24.0740
50
101.8618
20
3.7087
60
23.1481
21
25.8611
51
106.3055
21
40833
51
24.0633
22
27.7087
52
108.8148
22
44816
62
25.0370
23
29.6018
53
112.3796
23
48981
53
26.0092
24
31.5555
54
116.0000
24
6.3333
54
27.0000,
26
33.5648
55
119.6759
25
5.7869
66
28.0092
26
35.6296
56
123.4074
26
6.2592
66
29.0370
27
37.7500
67
127.1944
27
6.7500
67
30.0833
28
39.9259
68
131.0370
28
7.2592
68
31.1481
29
42.1574
69
134.9361
29
7.7669
89
a2.2314
30
<
44.4444
60
138.8688
30
a33&3
60
33.3333
( chii. )
BASE 35— SLOPE If to 1.
t
s
Add.
Height
Add.
Dif. of
Uti.
Deduct.
Dif. of
Uts.
Deduct.
1
.6805
31
51.2361
1
.0108
31
10.3811
2
1.4259
32
53.9250
2
.0432
32
11.0617
3
2.2361
33
56.6805
3
.0972
33
11.7638
4
3.1111
34
59.5000
4
.1728
34
12.4876
6
4.0609
35
62.3842
6
.2700
35
13.2330
6
5.0555
36
65.3333
6
.3889
36
14.0000
7
6.1250
37
68.3472
7
.5293
37
147885
8
7.2592
3^
.71.^59
8
.6913
38
15.5987
9
8.4583
39
745694
9
.8750
39
l&4a06
10
9.7222
40
77.7777
10
1.0802
40
17.2839
11
11.0509
41
81.0609
11
1.3071
41
1&1689
12
12.4444
42
. 843888
12
1.5555
^
19.0555
13
13.9028
43
87.7916
13
1.8256
43
19.9747
14
15.4259
44
91.2592
14
2.1173
44
20.9135
15
17.0138
45
947916
15
2.4305
45
21.8750
16
18.6666
46
«IC)«eJv$Oo
16
2.7654
46
22.8580
17
20.0509
47
102.0509
17
3.1219
47
23.8626
18
22.1666
48
105.7777
18
3.5000
48
248888
19
240138
49
109.5694
19
3.8997
49
25.9367
20
25.9259
50
113.4259
20
43210
50
27.0061
21
27.9028
51
117.3472
21
47639
51
28.0972
22
29.9444
52
121.3333
22
5.2284
52
29.20%
23
32.0509
53
125.3842
23
5.7145
53
30.3441
24
34.2222
54
129.5000
24
6.2222
54
31.5000
25
36.4583
55
133.6805
25
&7516
55
32.6774
26
38.7592
56
137.9259
26
7.3024
56
33.8765
27
41.1250
57
14J.2361
27
7.8750
57
35.0972
28
4a5dd5
58
146.6111
28
8.4691
58
36.3394
29
46.0509
59
151.0509
29
9.0848 50
37.6033
30
48.6111
60
155.5555
30
9.72^ 60
38.8888
( clviii. )
BASE 35-SLOPE 2 to 1.
1
Add.
1
Add.
s
1
Dedact,
a
31
Deduct.
1
.6851
81
666861
.0123
11.8642
2
1.4444
32
68.6666
2
.0494
32
12.6419
8
2.2777
33
61.7222
3
.1111
33
18.4444
4
3.1851
34
64.8518
4
.1976
34
14.2716
5
4.1666
36
68.0656
6
.3086
36
15.1284
6
6.2222
36
71.3333
6
.4444
36
l&OOOO
7
&3518
87
74.6851
7
.6049
37
1&9012
8
7.5555
38
78.1111
8
.7901
88
17.8271
9
8.8333
39
81.6111
9
1.0000
39
18.7777
10
10.1851
40
86.1851
10
1.2346
40
19.7530
11
11.6111
41
88.8333
11
1.4938
41
20.7630
12
13.1111
42
92.5555
12
1.7778
42
21.7777
13
14.6861
43
96.3518
13
2.0864
43
22.8271
14
16.8333
44
100.2222
14
2.4197
44
23.9012
15
18.0555
46
104.1666
15
2.7778
46
25.0000
16
19.8518
46
108.1851
16
3.1605
46
26.1234
17
21.7222
47
112.2777
17
8.6679
47
27.2716
18
23.6666
48
116.4444
18
4.0000
48
28.4444
19
25.6851
49
120.6851
19
4.4668
49
29.6420
20
27.7777
60
125.0000
20
4.9382
50
30.86^
21
29.9444
51
129.3888
21
5.4444
61
32.1111
22
32.1851
52
133.8618
22
6.9753
62
33.3827
23
34.5000
53
138.3888
23
6.6309
63
34.6790
24
3&8888
64
143.0000
24
7.1111
64
36.0000
25
38.2407
56
147.6851
25
7.7160
55
37.8456
26
41.8888
56
152.4444
26
8.3467
56
38.7100
27
44.5000
57
157.3888
27
9.0000
67
40.1111
28
47.1851
68
162.1851
28
9.6790
58
41.5308
29
49.9444
59
167.1666
29
10.3827
69
429758
30
52.7777
60
172.2222
30
11.1111
60
44.4444
"■
1
( clix. )
BASE 35 SLOPE 2J to 1.
■
1
93
Add.
1
31
Add.
Dif.of
Hts.
Deduct.
Dif.of
Hts.
Deduct.
■
1
.6944
645833
1
.0164
31
148302
2
1.4814
32
68.1481
2
.0617
32
16.8013
k
3
2.3611
33
71.8055
3
.1389
33
16.8056
4
3.3333
34
75.6565
4
.2468
34
17.8305
6
4.3981
35
79.3981
5
.3867
35
18.9043 \
6
5.5555
36
83.3333
6
.5565
36
20.0000
7
a8056
37
87.3611
7
.7661
37
21.1265
8
8.1481
38
91.4814
8
.9876
38
22.2839
9
9.5833
39
96.6944
9
1.2500
39
23.4722
10
11.1111
40
100.0000
10
1.6432
40
24.6913
11
12.7316
41
104.3981
11
1.8673
41
26.9413
12
14.4444
42
108.8888
12
2.2222
42
27.2222
i
13
16.2600
43
113.4722
13
2.6080
43
28.5360
t
14
18.1481
44
118.1481
14
3.0247
44
29.8766
r
16
20.1388
45
122.9166
15
3.4722
46
31.2500
16
22.2222
46
127.7777
16
3.9606
46
32.6543
17
24.3981
47
132.7316
17
44699
47
340896
1
18
2&6666
48
137.7777
18
6.0000
48
35.5555
19
29.0277
49
1^.9166
19
6.5710
49
37.0524
1
20
31.4814
50
148.1481
20
6.1728
50
38.6802
21
340277
51
153.4722
21
6.8066
61
40.1388
*
22
3&6666
62
168.8888
22
7.4691
62
41.7283
23
39.3981
63
1643981
23
8.1636
63
43.3487
24
42.2222
64
170.0000
24
8.8889
54
46.0000
25
45.1388
56
176.6944
26
9.6465
66
4&6820
26
48.1481
56
181.4814
26
10.4321
66
48.3950
1
27
61.2600
57
187.3611
27
11.2600
57
60.1388
28
54.4444
58
193.3333
28
12.0587
58
61.9135
29
57.7316
69
199.3981
29
12.9782
59
53.7191
30
«
61.1111
60
205.5566
30
13.8889
60
66.6556
( die. )
BASE 85— SLOPE 3 to 1.
1
n
1
Add.
1
n
Add.
1
Dednot.
til
Deduct
.7087
31
73.4814
.0185
81
17.7963
2
1.5186
32
77.6296
2
.0740
82
18.9630
3
2.4444
83
81.8888
8
.1667
33
20.1666
4
3.4814
34
86.2592
4
.2963
34
21.4074
6
4.6296
85
90.7407
5
.4628
35
22.6851
6
5.8888
86
95.3833
6
.6667
36
24.0000
7
7.2602
87
100.0370
7
.9074
87
25.3518
8
8.7407
38
104.8518
8
1.1852
38
2a7407
9
10.3833
39
109.7777
9
1.5000
39
28.1666
10
12.0370
40
1148148
10
1.8518
40
29.6296
11
18.8518
41
119.9629
11
2.2407
41
31.1296
12
16.7777
42
126.2222
12
2.6667
42
32.6666
13
17.8148
43
130.6925
13
8.1296
43
34.2407
14
19.9629
44
136.0740
14
3.6296
44
35.8518
15
22.2222
45
141.6666
15
41667
45
37.6000
16
245925
46
147.3703
16
47407
46
39.1851
17
27.0740
47
153.1851
17
5.3518
47
40.9074
18
29.6666
48
169.1111
18
6.0000
48
^.6666
19
32.3703
49
165.1481
19
a6852
49
44.4629
20
35.1851
50
171.2962
20
7.4074
50
46.2963
21
38.1111
61
177.5555
21
8.1667
51
49.1666
22
41.1481
62
183.9259
22
8.9629
52
60.0740
23
44.2962
53
190.4074
23
9.7962
53
52.0185
24
47.5555
54
197.0000
24
10.6667
54
64.0000
25
60.9269
55
203.7037
25
11.6741
55
56.0184
26
54.4074
66
210.6185
26
12.5184
56
58.0740
27
58.0000
67
217.4444
27
13.5000
57
60.1666
28
61.7087
68
224.4814
28
145185
68
62.2962
29
65.5185
59
231.6296
29
15.6741
59
64.4629
30
1
69.4444
60
238.8888
30
16.6667
60
66.6666
( clxi. )
BASE 36— SLOPE i to 1. |^
Add.
■a
•s
Add.
•9»
Deduct.
if of
Hts.
Dednct.
s
s
1
o
31
1
.6712
31
25.1157
.0015
1.4830
2
1.3518
32
2ft 0740
2
.0062
32
1.5802
8
2.0416
33
27.0416
3
.0139
33
1.6805
4
2.7407
34
28.0185
4
.0246
34
1.7839
5
3.44U0
35
29.0046
5
.0385
35
1.8904
6
4.1666
36
30.0000
6
.0555
36
2.0000
7
4.8935
37
31.<X>46
7
.0766
37
2.1126
8
5.6296
38
32.0185
8
.0988
38
2.2284
9
6.3750
39
33.0416
9
.1250
39
2.3472
10
7.1290
40
34.0740
10
.1643
40
2.4691
11
7.8935
41
35.1157
11
.1867
41
2.5941
12
8.666.)
42
36.1666
12
.2222
42
2.7222
13
9.4490
43
37.2268
13
.2608
43
2.8546
14
10.2407
44
38.2962
14
.30-25
44
2.9876
15
11.0416
45
39.3760
15
.3472
46
3.1250
16
11.8518
46
40.4629
16
.3951
46
3.2654
17
12.6712
47
41.5601
17
.4460
47
3.4089
18
13.5000
48
42.6666
18
.5000
48
3.5555
19
14.3379
49
43.7824
19
.5571
49
3.7052
20
15.1851
50
44.9074
20
.6173
50
3.8680
21
ia0416
51
46.0416
21
.6805
51
4.0139
22
16.9074
o2
47.1851
22
.7469
52
4.1728
23
17.7824
53
48.3379
23
.8163
53
4.3349
24
18.6666
54
49.6000
24
.8889
54
4.5000
25
19.5601
55
60.6712
25
.9647
55
4.6682
26
20.4629
56
51.8518
26
1.0432
56
4.8396
27
21.3750
57
53.0416
27
1.1260
57
6.0139
28
22.2962
58
642407
28
1.2099
68
6.1913
29
23.2268
59
66.449a
29
1.2978
69
5.3719
30
24.1666
60
56.6666
30
1.3889
60
5.6565
( dxii. )
BASE 36— SLOPE ^ to 1.
M Height
1
Add.
Hdght
Add.
Dif. of
Htf.
1
Dednet
Dif. of
Hts.
Deduct.
.6750
31
29.5648
1
.0031
31
2.9660
3
1.8703
32
30.8148
2
.0123
32
3.1606
3
2.0683
38
32.0633
3
.0278
33
33611
4
2.8148
84
33.8703
4
.0494
84
3.5679
6
3.5648
36
84.6759
5
.0772
36
3.7808
6
43338
86
36.0000
6
.1111
36
4.0000
7
6.1203
87
37.3425
7
.1612
37
4.2263
8
5.9250
88
38.7087
8
.1976
38
4.4568
9
6.7600
39
40.0838
9
.2500
39
4.6944
10
7.5926
40
41.4814
10
•«K/oD
40
4.9388
11
8.4687
41
^8981
11
.3734
41
6.1883
12
9.3338
42
44.3338
12
.4444
42
6.4444
13
10.2816
48
45.7870
13
.6216
43
6.7067
14
11.1481
44
47.2692
14
.6049
44
5.9758
15
12.0883
45
48.7500
15
.6944
46
6.2500
16
18.0970
46
50.2592
16
.7901
46
6.5308
17
14.0092
47
51.7870
17
.8920
47
ft8179
18
16.0000
48
63.3333
18
1.0000
48
7.1111
19
16.0092
49
64.8981
19
1.11^
49
7.4105
90
17.0370
50
5&4814
20
1.2346
50
7.7160
21
18.0838
51
68.0633
21
1.8611
61
8.0277
' 22
19.1481
62
89.7087
22
1.4938
62
8.3456
28
20.2816
53
61.3425
23
1.6327
53
8.6697
24
21.3333
54
63.0000
24
1.7778
54
9.0000
25
22.4587
55
64.6769
25
1.9296
66
9.3364
26
28.5926
56
66.8703
26
2.0864
66
9.6790
37
24.7500
57
68.0838
27
2.2600
67
10.0277
28
26.9269
58
69.8148
28
2.4197
68
10.3827
29
27.1203
59
71.6648
29
2.5966
69
10.7438
30
28.3888
60
78.3333
30
2.7778
60
11.1111
( clxiii
•)
BASE 36— SLOPE } to 1.
1
•s
Add.
Add.
Deduct.
Dednet.
a
1
a
Q
Q
.6805
31
34.0138
1
.0046
31
44^0
2
1.3888
32
a5.6556
2
.0185
32
47407
3
2.1250
33
37.1260
3
.0416
33
6.0416
4
2.8888
34
38.7222
4
.0740
34
6.3518
5
3.6805
35
40.3472
6
.1167
86
6.6712
6
45000
36
'^.0000
6
.1667
36
6.0000
7
6.3472
37
43.6806
7
.2268
87
&3379
8
6.2222
38
46.3888
8
.2963
38
6.6861
9
7.1250
39
47.1260
9
.3760
39
7.0416
10
8.0556
40
48.8888
10
.4630
40
7.4074
11
9.0138
41
60.6806
11
.6602
41
7.7824
12
10.0000
42
52.6000
12
.6667
42
8.1666
13
11.0138
43
54.3472
13
.7824
43
8.5602
14
12.0565
44
56.2222
14
.9074
44
8.9^29
15
13.1250
45
58.1250
16
1.0417
45
9^760
■
16
14.2222
46
60.0666
16
1.1852
46
9.7962
17
16.3472
47
62.0138
17
1.3379
47
10.2268
18
16.5000
48
64.0000
18
1.6000
48
10.6666
19
17.6805
^
66.0138
19
1.6713
49
11.1157
20
18.8888
60
68.0555
20
1.8518
60
11.5740
21
20.1250
61
70.1250
21
2.0417
61
12.0416
22
21.3888
52
72.2222
22
2.2407
52
12.6185
23
22.6805
63
743472
23
2.4491
53
13.0046
24
24.0000
64
76.5000
24
2.6667
54
13.5000
26
25.3472
55
78.6805
25
28935
65
14.0046
26
26.7222
56
80.8888
26
3.1296
66
145186
27
28.1250
67
83.1250
27
3.3760
67
16.0416
28
29.5666
58
86.3888
28
3.6296
68
15.6740
29
31.0138
69
87.6805
29
3.8935
m
iail67
30
32.6000 1 60
90.0000
30
41667 1 60
1&6666
■
( cxliv. )
BASE 36— SLOPE 1 to 1.
1
Add.
1
Add.
Deduct.
if. of
Deduct.
n
n
1
«
1
.6851
31
38.4629
J0062
31
6.9321
2
1.4074
32
40.29^
2
.0247
32
6.3210
8
2.1666
88
42J666
8
.0655
33
6.7222
4
2.9629
84
44.0740
4
.0988
34
7.1358
6
3.7962
35
46.0185
5
.1543
35
7.5617
&
4.6666
36
48.0000
6
.2222
86
8.0000
7
5.6740
37
50.0185
7
.8025
37
8.4506
8
6.6186
38
62.0740
8
.3961
38
a9136
9
7.6000
89
541666
9
.6000
39
9.3888
10
8.6185
40
56.2962
10
.6173
40
9.8765
11
9.5740
41
58.4629
11
.7469
41
10.3765
12
10.6666
^
60.6666
12
.8889
42
10.8888
18
11.7962
43
62.9074
13
1.0432
43
11.4135
14
12.9629
44
65.1861
14
1.2099
44
11.9506
15
141666
45
67.5000
15
1.3889
46
12.5000
16
15.4074
46
69.8518
16
1.5802
46
13.0617
17
16.6851
47
72.2407
17
1.7839
47
13.6368
18
18.0000
48
74.6666
18
2.0000
48
14.2222
19
19.3518
^
77.1296
19
2.2284
4»
148209
20
20.7407
60
79.6296
20
2.4691
50
16.4321
21
22.1666
61
82.1666
21
2.7222
51
16.0556
22
23.^296
52
84.7407
22
2.9876
52
16.6913
23
26.1296
63
87.3518
23
3.2664
63
17.3395
24
26.6666
54
9aoooo
24
3.5665
54
18.0000
25
28.2407
56
92.6861
26
3.8580
56
18.6728
26
29.8518
66
95.4074
26
41728
66
19.3680
27
31.5000
67
98.1666
27
4.6000
67
20.0665
28
33.1851
68
100.9629
28
48396
58
20.7654
29
34.9074
69
103.7962
29
6.1913
69
21.4876
30
36.6666
60
106.6666
30
5.6565
60
22.2222
( CIXT. )
BASE 36— SLOPE 1^ to 1.
Add.
Add.
Dif. of
Deduct
Dif. of
Uti.
Deduct.
1
.6898
31
^9120
.0077
81
7.4161
2
1.4259
32
46.0370
2
.0309
32
7.9012
3
2.2063
33
47.2063
3
.0694
33
8.4027
4
3.0370
34
49.4259
4
.1234
34
8.9197
5
3.9120
36
61.6898
5
.1928
36
9.4621
6
4.8333
36
64.0000
6
.2778
36
10.0000
7
5.8009
37
56.3564
7
.3781
37
10.6632
8
6.8148
38
68.7592
8
.^38
88
11.1419
9
7.8750
39
61.2083
9
.6250
39
11.7861
10
8.9814
40
63.7037
10
.7716
40
12.3456
11
10.13^
41
66.2463
11
.9336
41
12.9706
la
11.3333
42
68.8333
12
1.1111
42
13.6111
13
12.6787
43
71.4676
18
1.3040
48
14.2680
14
13.8703
44
74.1481
14
1.5123
44
14.9382
15
16.2063
46
76.8750
15
1.7361
46
15.6260
16
166925
46
79.6481
16
1.9763
46
16.3271
17
18.0231
47
82.4675
17
2.2299
47
17.0447
18
19.6000
48
86.3333
18
2.5000
48
17.7777
19
21.0231
49
88.2463
19
2.7865
49
18.5262
20
22.5925
60
91.2037
20
3.0864
60
19.2901
21
24.2083
51
942083
21
8.4028
61
20.0694
22
26.8703
62
97.26^4
22
8.7346
52
20.8641
28
27.5787
63
100.3564
23
4.0818
68
21.6743
24
29.3333
64
103.6000
24
4.4444
64
22.5000
25
31.1342
65
106.6898
25
4.8228
65
23.3410
26
32.9614
56
109.9269
26
6.2160
66
24.1975
27
34.8750
67
113.2083
27
5.6250
57
25.0694
28
36.8148
58
116.6370
28
6.0494
68
25.9567
29
38.8009
59
119.9120
29
6.4891
69
268696
SO
40.8333
60
123.3333
30
69444
60
27.7777
( olxvi. )
BASE 36— SLOPE 1^ to 1.
}
m
1
Add.
1
Add.
1
Dednet.
l«
Deduct.
.6844
31
47.3611
.0092
81
8.8961
2
1.4444
82
^.7777
2
.0370
32
9.4815
8
2.2500
83
52.2600
3
.0833
83
10.0833
4
3.1111
34
54.7777
4
.1480
84
10.7037
6
4.0277
85
57.3611
6
.2313
86
11.3^25
6
5.0000
86
60.0000
6
.3333
86
12.0000
7
6.0277
37
62.6944
7
.4537
87
12.6759
8
7.1111
38
65.4444
8
.5926
38
13.3708
9
8.2500
39
68.2500
9
.7500
89
14.0833
10
9.4444
40
71.1111
10
.9269
40
14.8148
11
10.6944
41
740277
11
1.1208
41
15.5648
12
12.0000
^
77.0000
12
1.3333
^
16.3333
13
13.3611
43
80.0277
13
1.6648
43
17.1202
14
14.7777
44
83.1111
14
1.8148
44
17.9269
15
16.2500
45
86.2500
15
2.0633
45
18.7500
16
17.7777
46
89.4444
16
2.3704
46
19.5925
17
19.3611
47
92.6944
17
2.6769
47
20.4587
18
21.0000
48
96.0000
18
8.0000
48
21.3333
19
22.6944
49
99.3611
19
8.3426
«
22.2314
20
24.4444
50
102.7777
20
8.7037
50
28.1481
21
26.2500
61
106.2500
21
4.0883
61
240888
22
28.1111
52
109.7777
22
4.4815
62
25.0370
23
30.0277
53
113.3611
23
4.8981
63
26.0092
24
32.0000
64
117.0000
24
5.3333
54
27.0000
26
34.0277
55
120.6944
26
6.7869
66
28.0092
26
36.1111
66
124.4444
26
6.2592
56
29.0370
27
38.2500
57
128.2600
27
6.7500
67
80.0833
28
40.4444
58
132.1111
28
7.2692
58
31.1481
29
•^.6944
59
136.0277
29
7.7869
59
82.2314
30 45.0000
60
140.0000
30
8.3833
60
3.33333
( clxvii. )
BASE 36— SLOPE If to 1.
t
s
Add.
n
Add.
Dif. of
Ht).
Dednct.
gas
Dednct.
1
.6990
31
51.8101
1
.0108
31
10.3811
2
1.4629
32
54.5185
2
.0432
32
11.0617
»
2.2916
33
57.2916
3
.0972
33
11.7638
4
3.1852
34
60.1296
4
.1728
34
12.4876
6
4.1435
35
63.0325
5
.2700
35
13.2330
6
5.1666
36
66.0000
6
.3889
36
14.0000
7
&2456
37
69.0625
7
.^93
37
147885
8
7.4074
38
72.1296
8
.6913
38
15.5987
9
8.6250
30
75.2916
9
.8760
39
16.4305
10
9.9074
40
78.5185
10
1.0802
40
17.2839
11
11.2456
41
81.8101
11
1.3071
41
18.1689
12
12.6666
42
85.1666
12
1.6555
42
19.0666
13
141435
43
88.5879
13
1.8256
43
19.9747
14
15.6852
44
92.0740
14
2.1 173
44
20.9135
15
17.2916
45
95.6250
15
2.4305
45
21.8750
16
18.9629
46
99.2407
16
2.7664
46
22.8680
17
20.6990
47
102.9212
17
3.1219
47
23.8626
18
22.6000
48
106.6666
18
3.5000
48
24.8888
19
243657
49
110.^68
19
3.8997
4ld
25.9367
2U
2&29e2
50
1143518
20
43210
60
27.00,61
21
28.2916
51
118.2916
21
47639
61
28.0972
22
30.3518
52
122.2962
22
5.2284
52
29.2098
£3
32.4768
53
126.3657
23
5.7145
63
30.3441
24
34.6666
54
130.5000
24
&2222
64
31.6000
25
36.9212
55
1346990
25
6.7616
55
32.0774
26
39.2407
56
138.9(^
26
7.3024
66
33.8765
27
41.6250
67
143.2916
27
7.8760
57
36.0972
28
440740
58
147.6852
28
8.4691
56
36.3394
29
46.5879
59
152.1435
29
9.08^
59
37.6033
ao
49.16661 60
156.6666
30
9.7222
60
38.8888
( clxviii. )
BASE 86— SLOPE 2 to 1.
eight
Add.
1
Add.
if. of
ite.
Deduct.
if. of
Deduct.
n
1
s
81
1
|Q
.7037
66.2592
.0123
31
11.8642
2
1.4814
82
59.2692
2
.0494
82
12.6419
3
2.3333
33
62.33:38
8
.1111
33
13.4444
4
3.2592
84
66.4814
4
.1976
34
14.2716
5
4.2692
35
68.7037
5
.3086
35
16.1234
6
6.8333
36
72.0000
6
4444.
36
16.0000
7
6.4814
37
75.3703
7
.6049
37
16.9012
8
7.7037
38
78.8148
8
.7901
88
17.8271
9
9.0000
39
82.3333
9
1.0000
39
18.7777
10
10.3703
40
85.9269
10
1.2346
40
19.7630
11
11.8148
41
89.5926
11
1.4938
41
20.7680
12
13.3333
42
98.8333
12
1.7778
42
21.7777
13
14.9269
43
97.1481
13
2.0864
43
22.8271
14
16.5926
44
101.0370
14
2.4197
44
23.9012
15
18.3833
45
106.0000
15
2.7778
45
26.0000
16
20.1481
46
109.0370
16
3.1606
46
26.1284
17
22.0370
47
113.1481
17
3.6679
47
27.2716
18
24.0000
48
117.8333
18
4.0000
48
28.4444
19
26.0370
49
121.6925
19
4.4668
49
29.6420
20
28.1481
60
126.9269
20
4.9382
50
80.8642
21
30.3333
51
180.3333
21
5.4444
61
82.1111
22
32.5925
62
134.8148
22
6.9758
62
33.3827
23
34.9269
63
139.3703
23
6.5309
63
34.6790
24
37.3338
54
144.0000
24
7.1111
64
36.0000
26
39.8148
55
148.7087
26
7.7160
65 .
37.8456
26
42.3708
66
163.4814
26
8.3457
66 :
38.7160
27
45.0000
57
168.3383
27
9.0000
67 '
40.1111
28
47.7037
58
163.2692
28
9.6790
58 '
41.5808
29
50.4814
59
163.2592
29
10.3827 59 1-
12.9758
80
53.3333
60 173.8833 |
80 11.1111 ' 60 [
144444
(clxi..)
BASE 36— SLOPE ^ to I.
1
Add.
1
Add.
I
Deduct.
Deduct.
1
.7129
31
66.1674
1
.0154
31
148302
2
1.6185
32
68.7407
2
.0617
32
15.8016
3
2.4166
33
72.4166
3
.1389
33
168055
4
3.4OT4
34
76.1851
4
.2468
34
17.8396
S
44907
36
80.0462
6
.3867
35
18.9043
6
5.6666
36
84.0000
6
.5565
36
20.0000
7
6.9361
37
88.0462
7
.7561
37
21.1265
8
8.2962
38
92.1851
8
.9676
38
22.2839
9
9.7500
39
96.4166
9
1.2500
39
23.4722
10
11.2962
40
100.7407
10
1.5432
40
24.6913
11
12.9351
41
105.1674
11
1.8673
41
25.9413
12
14.6666
42
109.6666
12
2.2222
42
27.2222
13
16.4907
43
114.2686
13
2.6080
43
28.6360
14
18.4074
44
118.9629
14
3.0247
44
29.8765
15
20.4166
45
123.7600
15
3.4722
43
31.2500
16
22.6186
46
128.6296
16
3.9506
46
326543
17
24.7129
47
133.6018
17
4.4599
47
34.0895
18
27.0000
48
138.6666
18
5.0000
48
36.6556
19
29.3796
49
143.8240
19
6.5710
49
37.0324
20
31.8518
60
149.0740
20
6.1728
60
38.6802
21
34.4166
51
164.4166
21
68055
31
40.1388
22
J7.0740
52
159.8518
22
7.4691
52
41.7283
23
39.8240
63
163.3796
23
8.1636
53
43.3487
24
12.6666
54
171.0000
24
8.8889
54
45.0000
23
15.6018
55
176.7129
26
9.6466
55 46.6820 ||
<M
OCtCMUt
w
lOORIOj;
Oft
flAWl
Kfl
taxinn 11
( clxx. )
BASE 36— SLOPE 3 to 1.
1
Add.
•a
•s
Add.
if. of
Ht8.
Deduct.
if. of
Elts.
Deduct.
SB
1
93
*
1
Q
.7222
31
74.0655
.0185
31
17.7963
2
1.5656
32
78.2222
2
.0740
32
18.9630
3
2.6000
33
82.6000
3
.1667
33
20.1666
4
3.5666
34
86.8888
4
.2963
34
21.4074
5
47222
35
91.3888
6
.4628
35
22.6851
6
&0000
36
96.0000
6
.6667
36
24.0000
7
7.3888
37
100.7222
7
.9074
37
25.3518
8
8.8888
38
105.5655
8
1.1852
38
26.7407
9
10.6000
39
110.6000
9
1.5000
39
28.1666
10
12.2222
40
115.6565
10
1.8518
40
29.6296
11
14.0565
41
120.7222
11
2.2407
41
31.1296
12
16.0000
42
126.0000
12
2.6667
42
32.6666
13
18.0556
43
131.3888
13
3.1296
43
34.2407
14
20.2222
44
136.8888
14
3.6296
44
35.8518
16
22.5000
45
142.5000
15
4.1667
45
37.6000
16
24.8888
46
148.2222
18
4.7407
46
39.1851
17
27.3888
47
154.0555
17
5.3618
47
40.9078
18
30.0000
48
160.0000
18
6.0000
48
^.6666
19
32.7222
49
166.0555
19
6.6852
49
44.4629
20
35.5555
50
172.2222
20
7.4074
50
46.2963
21
38.6000
61
178.5000
21
8.1667
61
49.1666
22
41.6655
62
184.8888
22
8.9629
52
50.0740
23
44.7222
63
191.3888
23
9.7962
63
62.0185
24
48.0000
64
198.0000
24
10.6667
54
54.0000
25
51.3888
55
204.7222
25
11.5741
56
56.0184
26
54.8888
66
211.5555
26
12.5184
56
68.0740
27
58.5000
57
218.5000
27
13.5000
57
60.1666
28
62.2222
58
226.5555
28
14.5186
58
62.2962
29
66.0555
59
232.7222
29
15.5741
59
64.4629
30
70.0000
60
240.0000
30 16.6667 1 60
66.6666
(
ci jxi. )
TABLE OF BASES.
I
Z
3
4
S
1
.0185
0370
.0556
.0741
.0920
2
.0370
0741
.1111
.1481
.1852
3
.0556
nil
.1667
.2222
.2778
4
.0741
1481
.2222
.2963
.3704
5
.0926
1852
.2778
.3704
.4630
6
.1111
2222
.3333
.4444
.6566
7
.1296
2593
.3889
.5186
.6481
8
.1481
2963
.4444
.5926
.7407
9
.1667
3333
.5000
.6687
.8333
10
.1852
3704
.5556
.7407
.9269
11
.2047
4074
.6111
.8148
1.0186
12
.2222
4444
.6667
1.1111
13
.2407
4816
.7222
!9630
1.2037
14
.2583
5185
.7778
1.0370
1.2963
15
.2778
3556
.8333
1.1111
1.3889
16
.2963
5926
.8889
1.1852
1.4816
17
.3148
6296
.9444
1.2592
1.5741
18
.3333
6667
1.0000
1.3334
1.6667
19
.3519
7037
1.05.56
1.4074
1.7692
20
.3704
7407
1.1111
1.4814
1.8518
21
.3889
7777
1.1687
1.5556
1.9444
22
.4074
8148
1.2222
1.6206
2.0370
23
.4259
8519
1.2778
1.7037
2.1297
24
.4444
8889
1.3333
1.7778
9.9-m.
25
.4630
9259
1.3889
1.8519
2.3148
( clxxii. )
TABLE OF BASES.
1
2
3
4 .
S
31
.5741
1.1481
1.7222
2.2963
2.8704
32
.5926
1.1852
1.7778
2.3704
2.9630
S3
.6111
1.2222
1.8333
2.4444
3.0556
34
.6296
1.2593
1.8889
2.5185
3.1481
35
.6481
1.2963
1.9444
2.5926
3.2407
36
.6667
1.3333
2.0000
2.6667
3.3333
37
.6852
1.3704
2.0556
2.7407
3.4259
38
.7037
1.4074
2.1111
2.8148
3.5185
39
.7222
1.4444
2.1667
2.8889
3.6111
40
.7407
1.4815
2.2222
2.9630
3.7037
41
.7593
1.5185
2.2778
3.0870
3.7963
42
.7778,
1.5556
2.3333
3.1111
3.8889
43
.7963
1.5926
2.3889
3.1852
3.9815
44
.8148
1.6296
2.4444
3.2592
4.0741
45
.8333
1.6667
2.5000
3.3334
4.1667
46
.8519
1.7037
2.5556
3.4074
42592
47
.8704
1.7407
-2.6111
3.4814
43518
48
.8889
1.7777
2.0667
3.5555
44444
49
.9074
1.8148
2.7222
3.6296
4.5370
50
.9259
1.8519
2.7778
3.7037
46297
51
.9444
1.8889
2.8333
3.7778
4.7222
52
.9630
1.9269
2.8889
3.8519
48148
53
.9815
1.9630
2.9444
3.9260
4.9074
54
1.0000
2.0000
3.0000
4.0000
5.0000
55
1.0185
2.0370
3.0556
4.0741
5.0926
56
1.0370
2.0741
3.1111
4.1481
5.18^
57
1.0556
2.1111
3.1067
4.2222
5.2777
58
1.0741
2.1481
3.2222
42963
5.3704
59
1.0926
2.1852
3.2778
4.3704
5.4630
60
1.1111
2.2222
3.3333
4.4444
5.5555
A,
" cd = he^ht at the other.
" bd = length of prismoid.
" abed ~ the vertical section through the
the direction of its length.
This figure is that view commonly represente
aad by reference to which all the calculatia
174
A section is a plot of a succession of levels taken along a
given line of country (see Fig. 2), shewing the comparative
levels of any two I points^ and also the distance between
them.
Fig. 2.
The line C D represents the datum line on a horizontal
plane^ assumed according to circumstances^ for the purpose
of shewing the comparative levels of any given places;
the line AB is the gradient determined to be worked on
by the engineer, which likewise has its comparative levels
in reference to the datum line C D ; the Ime E P is the
surface of the coimtry, consisting of hills and valleys on
the site of the line of the proposed work. According as the
gradient AB is below or above the surface of the country
EF, as shewn on the Fig. 2, the whole quantity of earthwork
is required to be taken from the space E ABF, if the former
case ; or it is necessary to fill up with earth, imposed on
the surface E F, a quantity sufficient to form the embank-
ment indicated on the section by the space AEBF. To
render the computation as simple as possible, and to reduce
it within the known rules of geometry, at every variation
of level there are perpendiculars let fall (or raised, as the
case may be) to the gradient AB, thereby making the
section a series of simple figures, and similar to that shewn
as Fig. 1, which is the prismoid. The ordinary way of
dividing the section is by squaring up lines with the datum
CD ; but if the gradient is not a level, but takes a direction
AB^, then the figure is no longer a rectangular prismoid
ABFE, (see Fig. 3) ; but a prismoid AB' FE where neither
the angles EAB* or AB^F axe right angles.
^e prismoid due to the sor&ce EF is greater in that
case than in the rectangnhtr caae : I will shew the difference
Airther on, and merely remark here, that in practice,
supposing snch difference existed in the prismoids, FG
represents the height due to a rectangnlar prismoid, while
PB' is the actual height measnred j the error is due to the
difference of the heights FB' and FG. Yet the steepest
gradient rarely exceeds 1 in 100; bo that when the per-
pendicular height FGwith the gradient is 1, the distance
GB' = -L, then the height PB' due to the perpendicular
to the base line is ^i + JL,; the error is so trifling that it
need never he regarded in calculations of this kind for
practical purposes.
When the sections are prepared, the slope of the aides
is determined upon according to the local and contingent
circumstances, and the base of the work is also given.
These are the only other quantities involved which are not
represented on the section; for on inspection of Pig, 1, it
is seen that the area ABCD of the transverse section
consists of a parallelogram of the base B Cj and height B I,
and two triangles of the height BI, and abase AI due to
the slcpe. Therefore, by knowing the heights on the section,
and the lengths, the cubic contents can be determined,
The rule given in books on geometry and o^
works is as follows : —
To the area of the two ends add four timt
section, and divide the sum by one-sixth of I
prismoid ; or (algebraically expressed)
(
176
Let H = height of one end.
" A = height of the other end.
" L = length.
" B = given base.
" S = given slope.
Then (HB + ffS + AB+ A^S + 4[(?J*) B + (iLlir)s]x|
is the cubic content of the prismoid.
When developed^ this equation becomes
[HB + ff S + AB+ A'S+ 2BH + 2BA + ff S^ 2HA+ A- S] + ^ ;
and when reduced^ it becomes
r(H+A)B (H« + H*+^5Sl T i.- ^ i.
I' — 2*-^ + ^ 3 — '""^ J L = cubic contents.
Now, this rule being given, in order to establish its
accuracy I will prove it by the method of fluxions, and
take it m the most simple form, when H = o, or the surface
of the ground at one end intersects the base (see Fig. 4).
^'^- ^' Let AB be the gra-
dient,* and AC the
surface, and the Ex-
pressions in algebra
^ bethesameasbefore.f
Let any variable area at DE be equal to y, and AD,
a variable length, be equal to x. Now ya? = fluxion of cube.
* In all cases where the gradient is mentioned, the formation level
is intended, which is generally 2 feet 6 inches lower than the level of
the rails. The word '' gradient" signifies a certain rise above, or foil
below, the horizontal line in some given length.
t These expressions will always be used throughout the whole
essay ; and, occcasionally, b, h, s, I are used, instead of B, H, S, L.
177
and as AB : AD : : BC : DE, or DE = ^: and the area
then 18 ( -J- + -p~) = y ; therefore —^ — + — p- =
fluxion of cube : the fluent of this is -j-j- -^ -j-p- = cube ;
and when x = 1, cube = "a" * ~ ~ ABC. Now, by
deducting the priam ADE from ABC, we can find
the priamoid EDBC. Introducing the other height
H, EDBC = i (»H , £|!) _ (»_» _ I») ,. BatDB
being giTen=L, x=l — Lj so, asa? : A :: L : (H — A) j tlierefore
, - At. = i — L, and ! - L ( Ji-J. Substitute
this value of L and 'a? in tte former equation,
1-7* 3 ' H— * ^3 3 ' H^
Bednce ttas, L (-^ ♦ -5- - -y - -j) - g^ -d
tterefore L (»- '!^) * -J '^') = ». But
, H"— y-lH + AjxCH— 4)ilience^^ = H + S. And
H<_tf=(H'*HJt»-) (H— 4)1 therefore ^■-H'tH»+A>.
Consequently ['ili«» * (iSjJUia
which is the same as the ordinary rule
For the benelil of those who do not
fluiiooal process, I subjoin a geometric n
178
Let fig. 5 be a prismoid in geometric perspective^ and the
slopes of the sides be assumed of equal ratio.
Fi«. 6.
I
The soKd figure is ABCDEFGH. The base of the work
being BC, draw perpendiculars to BC through B and C,
and complete the solid IBCKLMGFby the intersecting
vertical planes on B G and C F. The prismoid is then
divided into three figures^ namely^ the two equal soUds
AIBGMH, and DKCFLE, which are frustra of pyra-
nuds ; and the middle solid IBCKLMGF^ which is a
frustrum of a rectangular wedge. If the analysis is carried
on in the same manner as the former^ by assuming the
surface and the base to meet^ as in fig. 4, the results will
be obtained in a more simple form.
Using the same notation as before, we have —
h = height.
I = length.
s = ratio of slope,
b = base.
i
179
%.6-
I^ore 6 represents
the isoiQj^iic p»^6(s
tiTe of sQidi soEdy whoe
aQ the pboies meet at
FE.
First^ the wedge
HBCGEFis= ^'
Seo(nidfy,t]iepjnanid8AHBFaadDGCEue= ^
Therrfove the som is ^^ + ^-^ = cabe. This equation
bemg the same as prodnoed by the fluent in the fluxional
method, of conrae^ mnst bnng oat the same resnlts,
which, when detennined for a prismoidj becomes
j-6(H+j^ ^ |.(H*+H* + *«)]'*«• Mr, MacncB, in his
tables, has also proved the role in a different manner to
that followed hoe, though not in so concise a form of
investigation, and produces at once the role ordinarily given.
f^ Having now shewn the principle of the piismoidal
formula, I shall proceed to compare it with the ordinary
method of measuring work by contractors. There are two^
ways in use. One is to take the mean height of a section
(supposed to be subdivided), and, finding the area, then
to multiply by the length for the cube, or algebraically,
5±* =meaii height; [?i^+ (H'.aHA^y^^j^ j^^^
Compare this with the prismoid, and we find that the
quantities that differ are those due to the sides, therefore
4 — 3
3A2 + 12j? = 4ff + 4 HA + 4 As consequently
± 12 ^ = ff — 2HA + tf == (H — A)*. But as
(H — A)^ is always a positive quantity, the sign of the
other term of the equation lolLJMidHIBlis^i so that
180
X = j2 — "= *^® quantity required to be added to the
area of the mean height^ shewing that that process gives
the quantity less thw the true one. The second method
used by contractors is to find the areas of the ends of a
section^ and take the mean area^ and multiply by the length
as before for the cube^ or algebraically expressed^
|- BH.H»S.B*.yS j , i = eube = [B(Ha) . I (ff .^]/.
Comparing this with the prismoid^ it is the side quantities
that differ again; hence 5!l^ ± a? = 5Lt-5^
8H' + 3A* ± 6^ = 2H« + 2HA + 2A»; consequently
ff— 2HA + A' =+ 6ar=(H — A)»; and (H — A)« being
always positive^ x is always negative by transposition;
so that (lLzi*)Lf = quantity to be deducted from the
mean area founds proving that this method is always
in excess^ and^ comparing the two methods together,
the latter is twice as much in excess as the former is
in deficiency. As a numerical illustration may shew the
comparative results more clearly^ I will suppose two heights^
50 feet and 80 feet^ and a length 500 feet^ on a base 35
feet^ with a slope of 2 to 1.
By the prismoidal formula^
80 X 50 =- 1500 = HA
30 X 30
60 X 50
E>
900
2500
a)80= H + A
40
3)4900
1633i
2
_ H« + HS + A«
35 -B
3
= 8
1400 = b("'"
2
32661
so
30
181
3266|
600 = L
3333000
333
.,{
3)2333333
9) 777777.7
86419.7 cubic yardj.
By mean heights —
2)80
lo . 85 - 1400 = fflifiS
40 X 40 = 1600 « 2 = 3200 = EtiSf
4600-
(H + A) B (H 4- fl)" «
2 "^ 4
500
3)2300000
27 ri:
t 9) 766666| »^^
85185.1 c^'^J
Mean Heights = 85185.^;
Prismoid = 86419.^
Deficiency
182
By mean areas —
50 X 35 = 1750 1750 = BH
50 X 50 = 2500 X 2 = 5000 = H»«
50 X 35 = 1050 1050 = BA
30 X 30 = 900 X 2=1800 = /*'»
2)9600
4800 = 5i^ + 0^1^*
500
3)2400000
27 "
9) 800000
{
88888.8 cubic yards.
Mean areas = 88888.8 cubic yards.
Prismoid = 86419.7 "
Excess = 2469.1 cubic yards.
This single calculation shews that the error is very great
for such an ordinary length as 500 feet. A contractor
who uses these methods may, therefore, tender for a greater
quantity than is true by the method of mean areas ; and
by the method of mean heights, he may tender for a less
quantity than true : so that he incurs the danger of two
extremes — in the first case being liable to be refused,
because his figures exceed the estimate of the engineer,
based on the prismoidal formula ; and of being disadvan-
tageously met by other contractors, who may have availed
themselves of the true method ; or otherwise, if he should
tender according to the results derived in the second case,
and he should be accepted, he would find that, on his
work being measured, he would have to perform more
than he contracted for^ at his own cost; besides the general
183
effect the error in either case would have upon the schedule
of prices. On the other hand^ it is necessary that the
resident engineer should be careful not to allow the use
of the method of mean areas^ as the contractor would
thereby receive more money than his work performed would
warranty the contractor's interest evidently preventing him
firom using the other way. The consideration of the above
I therefore earnestly recommend to both parties^ that they
may do justice to each other as well as to themselves.
I have hitherto assumed that all the prismoidal sections
are rectangular^ although in page 175^ I alluded to cases
where they are otherwise^ owing to the inclination of the
gradient. Though at first sight the two cases may appear
to be alike^ yet the foUowing demonstration will explain
the difference. For simplicity^ I will assume the section
as in Fig. 7^ which represents an ordinarv small cuttings
commencing at the surface of the ground at A, the summit
being at B^ and the termination at C. Here A C is the gra-
Rg. 7. dient; and ABC is the
surface of the ground;
BD is a height which is
common to both pris-
moids ABD and DBC.
When AC is horizontal^
then BD is perpendicular
to it; but if the gradient takes another direction Kcy
being the same lengthy and the surface ABC being equal
to KbCy then 6rf, the perpendicular to Ac, is equal to
B D ; and i e, a vertical line through the point A, meeting
Ac in e, is greater than bd; for the angle bde being a
right angle, A e is the hypothenuse of the triangle bde^
and 6 e is also common to the prismoids A & e and ebc ;
but the lengths A c and A C are equal, and B D and b e
being given, the mean areas can be found, which multiplied
by the lengthy will give the cubic contents. Therefore,
because 6 e is greater than B D^ the solid A & c is greater
184
than the solid ABC. This result shews that the method
of squaring the divisions from the base line is not perfectly
accurate, ^ough, for the reasons previously given, suffi-
ciently so for practice.
It not unfrequently hi^peus that, in an irregular
country, the ground not only varies considerably in the
direction of the line of works, but also transversdy, so as
to affect the quantity to be measured in a very sensible
manner. In cases of this description, it is necessary to
take cross sections of the country at every sub-division of
the ordinary section, and sometimes oftener; on which
occasion the section must be further sub-divided to inter-
sect the cross sections.
In the subjoined Fig. 8, the line AB is the gradient
Fig. 8.
depressed below the sui&ce of the country, and the section
is sub-divided at various points a, a, a, into simple figures ;
and the lines ba, ba, ba, represent the cross sections at the
points a, a, a, having reference to perpendiculars at those
places, or toa hwizoatal datum line like an ordinarysection.
185
The most simple case of the prismoid with a cross sec-
tion is^ when two cross levels^ some measured distance
from each other^ produce the same inclination^ for then it
is sufficient to find the areas in the same manner as for
the common prismoid; but when two levels vary, then it
becomes necessary to determine the law of the variation,
and find the sohd by the fiuxional process, which is the
most ready method.
In Kg. 9, let the area ABCD represent a transverse
^^S< 9« section, where AD is
the natural slope of the
ground. Draw the hori-
zontal line LH, passing
through the centre (E)
of the section, EP is
the height of the section
at the centre of the base.
Let r be the ratio of the natural slope, when the vertical
height is = 1. The area ABCD consists of the triangle
ABN, the trapezium NBCO, and the triangle OCD.
Because EP is the mean between NB and OC, EP x BC
=area of NB CO. The triangle OCD = (EH— PC.) x ^ ;
BN
and the triangle ABN = (EK— BP) x — .
The slopes of the railway being assumed equal on
both sides, therefore EL = EG.
As EG: GI::r: 1 ::EH : HD.
AsGH = EH— EG : HD :: * : 1.
Hence EH = HD x r; therefore HD = M .
T
AlsoEH— EG = HD x s; therefore, HD = EH -EG
AndEH5 = EHr— EGr
EH (r— «)=EGr; therefore, EH = EG -I-, being the
width on one side of the centre.
A A
186
Afl EL : LM :: r : 1 :: EK : KA.
As KL =EL— EK : KA :: 8 : 1.
Hence EK == KA x r; therefore KA = —
Alao EL— EK = KA x «; therefore, KA = 51^=5?
And EK* = EL x r— EK x r
EK (r + «) = ELr; therefore, EK = EL-I-, or
EK = EG -^, being the width on the other side of the
centre.
Now since EG = |- + **>
WehaTeEH= *1^ {^^)
And EK= *^ (-^)
Also O C = EP * LC = A . I. = 2-^
And BN = EP-«/=A- i = ^^*.
From the above equations we derive the whole area ABCD
as follows
TheteiangleOCD= (^-±|Ai) (?^^) ^^_| (?4±i).
The triangle ABN = (AlfA.^) (^^^) l-^-| (^-A^^
Trapezium NBCO = A A,
Consequently, the whole area ABCD is —
When the slopes of the sides and the natural slope of
the ground are given, the area may be found speedily, if
they can be referred to the accompanying table. The
formula being simplified first into —
b± ^ 2j^b ^^^IizPyr ^^\) ; which, again reduced,
187
is T -^ ^^ [It^*] ' ^*' ''y expounding this
form, we have** + 4,^,AU2 (r'^^) 6>^,y ^^ g^^
and making J^. =X; i + /j-^^,, = Y; —J—^^=Z;
ff X + BHY + B'Z = area.
Slope 1 to 1.
Slope litoL.
Slope 2 to 1.
R
X
5
1.0416
10
1.0101
15
1.0044
20
1.0025
25
1.0016
30
1.0011
35
1.0008
40
1.0006
45
1.0005
50
1.0004
1.0416
1.0101
1.0044
1.0025
1.0016
1.001 1
1.0008
1.0006
1.0005
1.0004
R X
.01083
.00252
.00111
.00062
.00040
.00028
.00020 35
.OOOI5U0
.OOOI2U5
.oooiolso
5
10
15
20
25
30
1.6666
1.5345
1.5151
1.5085
1.5054
1.5037
1.5027
1.5021
1.5017
1.5013
1.1111
1.0230
1.0101
1.0056
1.0036
1.0025
1.0018
1.0013
1.0011
1.0008
R X
.01673
.00384
.00168
.00094
.00060
5
10
15
20
25
00042 30
.00030
35
00023 40
.00018
.00015
45
50
2.3810
2.0833
2.0363
2.0202
2.0129
2.0090
2.0065
2.0050
2.0040
2.0032
I.O9O6
r04l6
1.0181
1.0101
1.0064
1.0045
1.0032
1.0025
1.0020
1.0016
.02381
.00521
.00226
.00126
.00080
.00056
.00041
.00031
.00024
.00020
To render this table more comprehensible^ let us assume
a numerical example-
Let the height be 80 feet") And by referring to the table.
«
34 feetf slope 2 to 1, and opposite the
2 to 1 Rvalue of R, we find the respec-
35 to 1 3 tive coefficients X, Y, Z.
X X H2 = 900 X 2.0202 = 1818.18
Y X BH=1020 X 1.0101 = 1030.30
Z X B' = 1156 X .00126= 1.45
base
slope
Natural slope
9)2849.93=area in feet.
316.66=square yards area.
If the area had been computed, supposing the ground
to be level, then —
aa2
188
BH = 30 X 34 = 1020
H»x *= 30 X 30x2= 1800
9)2820
313.33 square yards.
Therefore^ this example shews^ that if the natural slope of
the ground had not been considered^ 3.33 square yards
would have been lost in the area. As the solid figure is
not altered in regard to its principles, by the consideration
of the natural ground slope, the cubic contents can be
found by modifying the formula for the simple prismoid.
For, using the same notation as before, and introducing the
second height, the solid is
= L X [B^Z + 2 + 3 J'
and if the mean areas of the ends be found, assuming them
to be calculated by the express formula for sloping ground,
the correct nile is [ A±J! _ (H-j^)^X j ^ j, = the solid,
when A and a are the areas of the ends.
Let this be illustrated
numerically :
H = 30 feet
A = 20 feet
In the table
we find —
B = 34 feet
X-
2.0129
S = 2 to 1
Y =
1.0064
R = 25 to 1
z =
.0008
L -400 feet
ff X = 900
X
2.0129 ==
1811.61
A^X = 400
X
2.0129 -
805.16
B(H+A)Y= 50 X
34
X 1.0064 -
1710.88
2 B' Z - 1156 "^
2
X .0008 =
1.85
2)4329.50
Mean area
—
2164.75
(H— A)'X X(30-20) '
2164.75 = mean area of the two ends.
33.54 ^ correction.
2131.21 =^ true mean area of prismoid.
400 = length.
f 9)852484.00 = contents in cubic feet.
i 3) 94720.44
31573.48 = cubic yards in solid.
Comparing this with the simple prismoid —
S H= = 900 X 2 - 1800
a A= = 400 X 2 - 800
B(H+A}= 50 ^ 34- 1700
2)4300
(H;
-hf.
= correction =
2160
33.33 -
2150 -«^ean area of the two ends.
'^' = 33.33
mean area.
correction.
2116.66 -
400 =
true mean area of the prismoid.
length.
9)846664.00 -
3) Mors.rr
contents in cubic feet.
31357.92 = cubic yards in solid.
By prismoid with sloping ground = 31573.';
By " level do. = 31357.i
Therefore, by this example, it appears that 21f
yards would be lost by neglecting to estimate for t
slope of 1^ gronnd.
190
Wlien the natural slope of the ground continually varies^
in order to determine the cube accurately, it is necessary
to ascertain the law of the variation of the slope ; which
process, if it were possible in practice, would involve so
many calculations, as to render it tedious and inapplicable
for practical men ; but it is a very near approximation to
the real value, if the natural slope of the ground is sup-
posed to increase directly in proportion to the distances.
Let Fig. 10 represent a transverse section of an uniform
Fig. 10. rising section. J£ we
suppose the base EC
to intersect a horizontal
ground surface trans-
versely, but as the sec-
tion advances, the cross
sections assume the
figures EBCF, GBCH,
ABCD, whose natural
ground slopes vary in proportion to the distance from the
intersecting point, through which BC passes; that is, if the
section EBCF is at half the distance at which ABCD is
situated, the ratio of 01 to IF is half the ratio of ML to
LD; and also if the ratio of NK to KH of the section
GBCH (whose centre point N is midway between M and
O) is half the sum, or the mean between the ratio ML to
LD, and O I to IF. Then if these ratios are given, it is
easy to determine the cube very nearly. For this solid
may be considered as only another modification of the
prismoid ; and whereas the increments of the heights and ^
slopes are uniformly proportional, we shall find that the
same relation exists between the prismoid and the rules
for mean heights or areas, as has been shown in former
examples. Therefore, making use of the former notation
and example, and adding a new ratio of slope r = 15 to 1
due to one of the ends, we have, by using the tables, the
following method to find the mean area : —
191
L = 400 feet.
H = 80 R = 25 B = 34
h=20 r = 15 S=2
H + h = 30+20 = 25 = A = mean height.
2 2
R+_r ^ 25_ii5 _ 20 ^ ^ ^ ^ej„ slope.
2 2
In the table we find the following coefficients : —
Due to R = 25.
X = 2.0129
Y = 1.0064
Z = .0008 z = .00226
H2 X = 900 X 2.0129 = 1811.61
'BHY = 34 X 30 X 1.0064 = 1026.53
Due to r = 15.
X = 2.0362
y = 1.0181
z =
y
z
Due to r = 20.
2.0202
1.0101
.00126
B^Z =1156x
.0008 =
.92
Px = 400
Bhy = 34 X 20
B z = 1156
(A)
2.0362 = 814.48
1.0181 = 692.31
.00226= 2.61
Area of
2889.06 5 greater
c end.
(B)
Area of
1509.40 { ^^^
A»a? = 625 X 2.0202 = 1262.62
BAy = 34x25 X 1.0101 = 858.58
B2 r = 1156 X .00126 = 1.45
Area of
(C) 2122.65x4=8490.60 J ™f-
c sec.
Calculation carried forward
2139.84
400
6)12839.06
Mean area 2139.84
c 8)855986.00
C 9)285312.00
31701.33 cube yards — true contents of solid;
192
Compare this with the mean height method^ we have
2122.65 Area (C)
400 cube yds.
By prismoid 81701.83
3)849060.00 By mean heights 81446.66
27'
9)283020.00 Deficiency 254.66
I
81446.66 cube yards.
And comparing it with the method of mean areas^ we
have—
2839.06 = greater end (A)
1509.40 = lesser end (B)
2)4348.46
2174.23 = mean area of the two ends.
400
cube yds.
3)869692.00 By prismoid 31701.33
27^ By mean areas 32210.81
9)289897.33
— . Excess 509.48
32210.81 cube yards.
I>i£Perence between mean heights and mean areas 764.15
cubic yards.
These results shew that, though not exactly correct, the
method by the prismoidal formiila is nearer the truth than
either of the other two, and the method is nearer and
nearer the usual result, as the given variable ratios of the
slopes approach to equality.
In case the formation of the surface assumes a curve, the
nearest method that can be used in practice is by laying
down such a straight line as will give the same area, and
determine the mean slope of the particular cross section :
this being repeated as often as may be necessary, the
remaining process is the same as before to find the cube.
193
If inagiven cross section there may be found two slopes
(rednced from a cmre or otherwise) whose intersection can
be conveniently determined, within two vertical lines fall-
ing on the extremities of the base; then the base being
subdivided by a line perpendicular to it, from the intersec-
tion of the slopes, two separate calculiUions may be made
of the respective areas, whose sum is equal to the whole
transverse section. Thus, in fig. 11, ABCD is a cross
^. !!• section, whose sur&ce
AED is composed of
two slopes AE, ED
meeting at E. The
base BC is dividedinto
twolengUis, BH, HC;
and the area ABCD
can be computed by
finding the sum of
ABHEandEHCD.
Now, as the mean height EH, at the intersection of the
slopes = H ; and BH, the part of the base cut oflF, can be
measured = b ; then substituting this height for the usual
height, and b for ?, the general expression for each figure
becomes (t±ML- *) x (*^^) * (?Iff^) *.
This equation reduced to its simplest terms is
(ftA+Z^ -+ — ). The sign plus being used in the
r . . ft'
coefficient 77+7, and the sign minus in the term + ^
when the ground/a/& towards the centre, and contrariwise
when the ground rises.
*
When the nature of the ground is such that it becomes
necessary to use two different slopes on opposite sides of
r + «
194
an embankment or cuttings it is sometimes convenieat to
compute the contents by taking half the snm of the cubes
produced^ supposing the section to be calculated with each
slope separately. But^ if the tables used admit di it, the
simplest way is to take the mean between the two given
slopes, and work out the cubes as usual. For as ^—
is the area of the one side. H^ (5jL£2 is the area of the
2
two sides. But in the case of inclining ground^ the slopes
must be separated^ as the equation of each side has a co-
efficient depending on the particular slope; therefore, the
rule given for the last case applies here, making A = ?
or half the base, if the inclination of the groimd is uniform.
It sometimes happens, after the estimates are completed,
that, owing to the insufficiency or improper disposal of
materials, according to the existing gradients and other
causes, the engineer alters the gradient, and thereby ren-
ders it necessary to undertake another series of calculations.
The easiest way is to make use of the prismoidal tables
with the amended heights ; but as it may be sometimes
useful to know the area due to the diiference of the heights^
I will subjoin a solution of this problem.
Let Fig. 12 represent a transverse section. ABCD is
l^iR- 12. the original area; and
BF is an increase in
depth, the base and
slopes remaining the
same. It is obvious
that the additional area
is the figure BFEC,
and twice CEGD. If
the parallelogram CEGH be completed, and HK drawn
perpendicular, and BC FE be produced to meet HK,
then the rectangular parallelogram CEKI is equal to
195
CEGH ; CEGD 18 equal to CEGH — the right-angled
triangle GHD. But DGis to GH as the ratio of the
slope; and CI is equal to the snm of the side base due
to the height + DG, or CI is the base dne to the increased
height. Therefore, in notation, making d = increase of
depth, we haveBE=A(*and'xCEK;i =2rf (A + rf) s— (fa;
therefore the increase of area i& d [b -^ {2h + cQ s] ;
or, if d represented the reduction of depth, the area to be
deducted is d [4+ (2A— d) s].
The next case which comes under our notice is, when
in any given section the dopes do not continue uniformly
{torn the gradient to the sur&ce of the ground, but are
interrupted by a bench being introdueed at a given point
of the height. Let fig. 13 represent such a cutting. AB
Fig. 13. isthebasejHGthesur-
. face; FC DE benches
introduced. Here, by
producing the slope
BD to meet the sur-
face in I, the psrallelo-
gram IGED is the ad-
ditional area to each side of the ori^al section. Therefore,
if the height <rfDE firom ABbeglTen=A', and the breadth
DF=ft,then2 (H — A') b = area to be added to the ormnal
section. K these benches extend in parallel planes wim the
gradient, then the additional soUd is ( H^*-3ft')6L
The last case but one I shall observe is, when the widths
in a plan are given, to find the cubic contents.
196
In the diagram Pig. U, let A BCD represent a plan of a
^*^' ^^' prismoid; and let the dotted
TTj lines represent the respec-
tive sections at the ends.
That is, let ABEP be the
section at AB ; andCDHG
be the section at CD. Pro-
duce FE HG both ways,
and let fall on them the
perpendiculars, completing
the rectangles A I K B,
C MLD. Insert W for A B,
and w for CD, and use in
other respects the previous
notation.
It appears by the construction that
WH— H2S = areaof ABEForAIKB— 2 AIP;
wh~hU = area of CDHG or CMLD— 2 CMG.
But W = 2 H« + B, therefore H = 5L=M.
^ffll j^ W^— WB H3 S = '^''— 2 WB H- B^
Therefore, the area AEBF = W^z:5!, and substituting
half the width and half the base for their respective wholes,
we have ^^^=2? = area ABEP.
s
Treating the other area in a similar manner, we find
CDGH = ^^-^—^i therefore, the solid contents of
A BP.PaTTT^n -c r^g^!=g . ^^^' . W^2\fw^vP^ w -x L.
\. s s s J^e
This equation reduced becomes [(WliZi^+u^ — ?' "I x L
It is to be observed that this equation is simpler than that
given in the terms of heights ; for as « and B are known,
197
th^e i« only one unknown terra, from which a constant
quantity is deducted, to find the mean area.
It only remains now to find the cubic contents of a
prismoid with sloping ground, when the extreme widths
are given. Let us assume a case where the slope is uniform
throughout.
Fig. 15,
Let Fig. 15 represent the proposed prismoid whose cube
is required. Let NK be a line parallel to the base EF,
intersecting the surface AB in I, the vertical centre of
the base, and cutting the slopes in M and N ; and let fall
the perpendiculars AE, B£, through A and B on the line
NK. By a former caae we know thatIL= IN (— ^1, and
IK=IN (-^^); therefore LK=IN(^). AlsoAB^Wis
the hypotbenuse of a triangle whose base and perpend icula r
are in the ratio of r to 1: theiefore AB ^ W = LK i"^^.)
IJet cLK ='W, when c is the coefficient ■ t -
,j,_BiiHS therefore W - tilH-S, J^
merefore H - '^fc^
198
By the fonner case the area vas found to foe
If half the base and half the width be given^ instead of
the whole base and widths and the value of H be substi-
tuted, we have area A =
and inserting the value of c in the equation —
Now as H = W (;7v^=^) — 7 $ a^d it may be
sometimes desirable to know the height in the middle, the
subjoined table is constructed in order to facilitate the
calculations.
The column X is computed by the formula (
r^—s^
s (r+H)
);
and the column C by the formula = ( . ^ )
Slope 1 to 1.
Slope Ij
to 1.
b:
X
C
R
X
C
6
.92308
.94137
5
.58334
.59490
10
.98022
.98487
10
.64523
.63368
15
.99115
.99337
15
.65708
.65855
20
.99502
.99625
20
.66195
.66278
25
.99680
.99760
25
.66379
.66423
30
.99780
.99835
30
.66461
.66498
35
.99838
.99877
35
.66490
.66518
40
.99875
.99907
40
,66531
.66553
45
.99900
.99926
45
.66560
M576
50
.99922
.99942
50
.66581
.66595
Slope 2 to 1.
R
5
10
15
20
25
30
35
40
45
50 I
.40385
.47524
.48893
.49377
.49601
.49723
.49796
.49843
.49876
.49900
C
.41185
.47762
.49002
.49439
.49641
.49751
.49817
.49860
.49890
.49910
I will illustrate this table by a numerical example :
Given, The natural slope R = 15 to 1.
Half the base = 17 feet.
Half the width = 108 feet.
The slope being = 2 to 1.
Here X = 0.M89S; tbnefiHc.
+ 108 X lOS X 0.48893 = 5702.88
— 17 K 17 « J = 144.50
Feet 5558.38 meu uea.
Nov C = 0.49002} therefore,
+ 108 - 0.49002 =- 52^
— 17-1 = 8.50
Feet 44.42 heiglit in the middle.
Having ibond the height, let us prove the preceding
calculation of the area hy the table given in page 187, in
the terms of the heights and base.
Here X = 3.0362 j Y = 1.0181; Z = .00226; therefore,
44.42 X 44.42 x 2.0362 = 4017.70
44.42 X 34 X 1.0181 -= 1537.62
34 X 34 X 0.00226 = 2.61
Feet 5557.93. mean area;
the difieience being only such as may be due to a
trifling error in the last place of decimals in the table.
The only difference in fiuding the solid in this case and
the last will be by affixing to the term in which W and
V? are found, the coefficients X due to the sloping ground,
instead of the coefficient ~ > the sohd then becomes
[.(^^±W^)_^"].
RULES RELATING TO THE PRISMOIDAL
FORMULA.
To avoid the necessity of referring to the essay "■ — '-
late cubic contents, I subjoin the following —
BTTLEB FOB PRACTICAL CASES.
1. — To find the contents of a primurid (
cross section is horizontal},
B H + H' s From the mean aiea of the two en
200
BA + A? S one-Bixth of the product of the slope^ multi-
2 plied by the square of the diflference of the
(H— .*)» S heights. This difiference multiplied by the
6 length will give the contents.
2. — To find the area of a transverse section of a
railway [when the cross section is horizontal).
B H + H' S Multiply the base by the height, and add
to the product the product of the slope and
the square of the height.
3. — To find the area of a transverse section {when
the cross section is sloping).
Let 1 to r be the ratio of the sloping grouud,
r being the horizontal length ; and let 1 to #
be the ratio of the slope of the cutting; then
making X = -3^^,, Y = 4 + -4^x
Z = 4 (y^ —s^Y "^^^ ^^^ "^^ ^® found by
H'X + HBY adding together the product of the square of
+ B'Z the height by X, the product of the base by
the height by Y, and the product of the
square of the base by L.
4. — To find the cubic contents of a prismoid (the
cross section being sloping).
A + g Prom the mean area of the two ends deduct
2 one-sixth of the product of the coefficient x
{U — h)^x (found by rule 3), and the square of the diflFer-
6 ence of the heights. The difference multiplied
^ L by the len^h gives the contents.
5. — To find the area due to an alteration in the level
of abase or formation line.
first Case. — If the depth is increased:
Multiply the sum of twice the original height,
rf[B+(2H+rf)«]and the increase of depth, by the slope; to
this add the base, and multiply the sum by the
increase of depth for the increase of area.
201
Second Case. — If the depth is diminished :
Multiply the difference of twice the original
height, and the diminution of depth, by the
d[B+(2ft-d)5]slope; to this add the base, and multiply the
sum by the diminution of depth; the result
gives the area to be deducted.
6. — To find the additional soUd by having benches
on each side (parallel with the base line),
(H+A — 2A*)6L From the sum of the heights deduct twice
2 the height of the bench above the base ; mul-
tiply the difference by half the width of the
bench, and by the length ; the product is the
contents.
7 — When the half-undths of the cuttings or embank-
ments at the edge of the slopes against the surface
are given, to find the area.
W^—B^ Divide the difference of the squares of half
s the width and half the base by the slope ;
the result is the area of the section.
8. — When the tvidths are given (as above), to find
the cubic contents.
W+Ww-^u^ Add together the square of half the greater
3 « width, the square of half the lesser width, and
the product of both half widths; divide this
__ B^ sum by 3, and from the quotient deduct the
s square of half the base. This difference divi-
ded by the slope, and multiplied by the length,
will give the cubic contents.
9. — When the tvidtlis are given, to find the area
{w?ien the cross section is sloping).
Let 1 to r be the ratio of the sloping ground;
and 1 to * be the ratio of the slopes of the
cutting ; make x = ^~" . Then the pro-
duct of the square of half the width, by the
B2 coefficient x, less by the quotient of the square
^ Y of half the base divided by the slope, is the area,
B B
202
10. — To find the height, given the width {when the
cross section between is sloping).
Wc — - Make C = ^5=^=, > ^^®^ *^® ground
is level, the coefficient C becomes = 1
then, by dividing half the base by the slope,
and deducting the quotient from the product
of half the width, and the coefficient C, the
result is the height in the middle.
11, — To find the width when the height is given {the
cross section of the ground being sloping) .
To the height add the quotient of half the
B hnsG divided by the slope, and divide the sum
7 by the coefficient C as before found; the
"C result is the width.
12. — When the uoidths are given, to find the cubic
contents {the cross section being sloping ground).
x{W^+Ww+w^ ) Proceed the same as in rule 8, substitut-
* ing for coefficient j the coefficient -; when
_ B- .r is found by the formula in rule 9. The result
7 is the cubic contents.
EXPLANATION
OF THE USB OP
TABLES OF EARTHWORK.
In preparing these tables^ the object I had in view was
to do away with the necessity of turning over many pages
and of referring to the intersection of two columns of given
heights to find the tabular number^ and also to serve other
useful purposes ; and I thought that if I could reduce the
table required for any given slope and base to one page^ I
should materially simplify the operations^ though appa-
rently at the expense of a few extiui figures. The tables of
Mr. Mac Neill are constructed partly for given bases and
slopes, and partly for abase 1, with a series of slopes. The
former tables, by reference to the intersection of the given
heights, at once produce the mpan area of the prismoid ;
but these tables are very limited in extent of base and
slope. The latter tables, by a similar reference, give a
number in one column to be multiplied by the given base,
and this is added to a number found in the same line of
intersection in a second column. The sum is the mean
area required. I here subjoin an example ; the two heights
B b2
J
204
being 18 and 38, and the slope being 1 to 1, &nd the basi
32 feet :—
By Second Serws of Tables.
In base 1, slope 1 to 1, opposite IS and under 38 ve find-
Tabular niunber . 1.037
Multiply by base . . 32
Add tabular number . . 30.272
Mean area . . 63.456
In using either series of tables it is necessary to turn
over a few pages eonatantly, which renders the application
tedious, though very far preferable to calculating by the
formula. These tables, moreover, do not admit of any
appbcation of them except for the purpose of cubing the
pnamoid.
Other tables have been published for computing the
quantities for any given base, but they are not more ad-
vantageous than Mac Neill's, but are more economical in
cost, and have been serviceable, owing to the present
scarcity of Mac Neill's work.
Mac Neill's tables are computed by the formula
/H + S\ - /H"+ HA + ft'\ , . , .„ .
^_ — 2 — J B + ^^^ — - — 3 ) a, which will give the
mean area in feet, and divided by 27 gives bis tabular
number in his first series of tables at each intersection
:n heights. In his second series, he has divided
ular numbers into two columns at each mtersec-
' the heights, the first bemg computed by the
5^ and the second by the term ( ^i ^ «•
dimensions are measured in feet.
205
As I wish to save as much as possible the intersecting
method, which, in a work of the extent I have brought
out, would have been abnost impracticable on account of
the labour and expense attending it, and being desirous of
applying the same tables to other purposes, I sought and
found the formula — ^ + 2 — 6
well adapted for the purpose. This is obviously the mean
area of the two ends, with the correction applied to render
the prismoid true, the particular investigation of which will
be found at page 180. By the use of this formula I keep
the heights independent of each other, except in the third
term, when their difference is required. Therefore in
determining the values of the terms for any series of bases,
slopes, and heights, the two first terms are exactly similar,
and can be classed in one table ; and the third term, de-
pending upon the difference of heights, can be classed in
a second table ; and this term is also common in all the
given bases for the same slope. But in the tables I have
reprinted it in every base, so as to save the trouble of
turning to another page. Therefore the tables are com-
BH + H«S
puted for the first two columns by the term — gj ,
and the table of differences by the term y^ In order
to use the tables the following rules are given : —
To Calculate the Oube.
Look in the table of the given base and slope opposite
the two given heights, for the numbers under the columns
headed '^ add,'^ and add these together : this corresponds
with the mean area of the two ends. Then look in the
columns headed '' deduct,^' for the number opposite the
difference of the heights : by deducting this from the sum
previously obtained, the mean area of the cube will be
found, which, multiplied by the length, wiU give the cubic
contents in yards. All the dimensions must be given in
206
feet. Take^ for an example^ the dimensions before given
in illustration of Mac Neill's tables —
Base 32, Slope 1 to 1.
Col. Add.
Opposite 18 we find . . . . 16.6666
Ditto 38 ditto . • . . 49.2592
65.9258
Col. Deduct.
Difierence of heights being 20, oppo-
site 20 we find .... 2.4691
Mean area . . . 63.4567
It is obvious, in comparing this method with Mr. Mac
Neill's, that the operation of adding and svhtracting, re-
quired by the former method, is much less liable to error
than the operation of multiplying and adding required by
the latter. Besides, the two added numbers at once give
an approximate result, which may frequently su£5[ce for a
rough estimate, without subtracting at all.
I now give a form which will illustrate the calculation
of a cutting or embankment complete. I used these
tables for some years on the Eastern Counties Railway ;
and for the convenience of preserving the calculations, I
had a number of books ruled in this form, in the manner
of a levelling book. .And the whole process admits of being
checked in a similar manner, except the multiplication :
for the sum of the columns of addition in columns 1 and 2
should equal the sum of the various sums column 3 ; and
the sum of the deductions, column 4, deducted from the
sum in column 3, should correspond with the sum of the
differences in column 5. The lengths are written in
column 6; and the product of columns 5 and 6 are
written in column 7 : the sum of these products will give
the quantity in the cutting or embankment. In columns
8 and 9 are written the respective heights at either end ;
and column 10 gives the difference of the heights.
Base
32, Slope 1 to 1.
1 2
3
5
6
7
8 9
10
Add (ogelhcr.
Bum.
Unglh.
Frodd.
S'H
DH. 01
BfBrt.
lu.rd..
hBlihu.
0,0000 2.6666
2.6666
.0968
2.5678
120
308
01 4
4
2.6666
5.9259
8.5925
.0988
8.4937
260
2208
4 ! 8
5.9529
14.2222
20.1481
.3951
19.7530
340
6716
8
16
8
14.2222
24.8888
S9.1110
.3951
38.7159
280
10840
16
24
8
24.88BB
37.9259
52,8147
.3951
61.4196
670
41151
24
32
14.2222
11.5259
25.7481
2.0000
23.7481
8?0
20661
16
14
18
11.5259
6.0555
16.5814
.5000
16.0814
460
7397
14
7
9
5.055S
1.9444
6.9999
.0988
6.9011
330
3277
7
3
1.94441 O.O0O0
1.9444
.0555
1.8889
130
246
31
3
Total
ubic yards—
91804
In the above form there IS no necessity to repeat bo many
of the figures, for it is obvious that the same height is
common to both adjoining prismoids, and the same tabular
nmnber will apply, except in such cases where a jump or
sudden break in the ground occurs at the same place as
illustrated in line six of the cdculation ; except in such a
case, it would be sufficient merely to write the numbers in
columns 2 and 9^ omitting those in columns 1 and 8. There-
fore for each priamoid two tabular numbers are required
to be abstracted, both found in tlie same page ; the one for
the last height of the prismoid, and the other for the
dijference of the he^hts. The number due to the first
ka.ght of the prismoid is the same as that due to the last
height of the prismoid immediately preceding, so that it
will have been already entered in the form. The quickest
way, having first transferred all the measurements to the
form, is to extract tlie tabular numbers at once s<
and then proceed to the addition, subtraction, and
plication of the whole. After a little practice th(
will soon become habituated to the tables. In j
three places of decimals are amply accurate. Th<
the tables, and of the above form, will be foiu
208
simple, if, instead of the lengths of each prismoid being
unequal, the given cutting or embankment was divided
into any number of equal parts; let the heights be
measured as usual, and the tabular numbers entered in
the form ; for then, in order to find the cube, sum up
column 8, from which deduct the sum of column 4, and
multiply by the whole length of the cutting or embank-
ment, and divide the product by the number of prismoids
of equal length : the quotient is the required cube. This
last method wiU probably reduce the calculation of a long
cutting or embankment to one operation of multiplication
{* ^!S^^^?i^^^ ^^ several, thereby considerably reducing the
J5Mffl9rt)|^error, and enabling the whole of the work to be
easily ch)^cked.
To Calculate the Area of the Section.
Multiply the tabular number in the columns headed
" add,^' opposite any given height in feet, by 6 j and the
product is the area in square yards. Hence in the
preceding form any of the numbers in columns 1 and 2
may be taken to find the area of the section ; for instance,
24.8888 X 6 = 149.3328 = area in yards, corresponding
with 24 feet height in column 8. The numbers in columns
1 and 2 themselves are half the cubic contents, in yards,
due to the section of a prism 1 foot long.
To Calculate the Area of the Sides.
Multiply the tabular number in the columns headed
^^ deduct,'* opposite any given height in feet, by 6; and
the product is the cubic contents, in yards, due to 1 foot
of length: this again multiplied by 3 will give the area of
the sides in yards.
The preceding form, therefore, enables us to take a
memorandum of the section, the base and slope and situa-
tion on the section being indicated at the head of the
form, the lengths and heights being given in columns 6,
8, 9 of the form ; also, to produce the sectional area at any
given place, or the area of the sides, or the cube.
209
As it may be required to know the area of any section^
supposing that the base is made accidentally narrower
or broader^ or to compute the cubic contents consequent
upon such alteration^ I subjoin a table of bases^ 1, 2,
Sy 4iy 5. By the use of this table^ suppose that it were
required to compute the cubic contents of a cutting with
base 18^ which is not in the table ; then compute as if
for base 20^ and deduct firom each calculation of the
mean area the sum of the two numbers due to the differ-
ence of the bases (20 — 18 = 2) opposite the given heights
in the tables of bases: the difference is the true mean area.
To find the area of any given section for an altered base^
deduct or add the number opposite the given height in the
column of bases which represents the decrease or increase^
from the tabular number of the given height in the
original base ; six times the result is the true area. To
find the area of the middle piece, multiply the number
opposite the given height in base 1 by the given base ;
six times the result is the area. And to find the cubic
contents of the middle piece add together the corresponding
numbers in base 1 due to the given heights, and multiply
by the length, and by the given base : the result is the
cube.
210
Having thus explained the use of the tables, 1 now
proceed to give an explanation of a scale for measuring
earthwork, which I have successfully used on
the Eastern Counties Bailway. The vertical
and horizontal scales, and also the hase and
slope, must be previously determined for each
scale, and then a set can be formed embnunng
the requiredslopesoftherailway. My scales
were made four in number, for base 84-;
slopes,], Ij, Ij, and 2 tol; and on the back
of each was properly described the slope,
base, and vertical and horizontal scales to
whitJi they were applicable. All the dimen-
sions were taken in yards lineal, superficial,
or cubical, as required ; the application being
precisely the same as the use of the tables,
and the rules being the same to iind the area,
using 2 as a coefficient instead of 6. The
annexed diagram shews one of the scales for
slope 1 to 1, reduced to one-half of its real
size, being calculated for 20 feet to I inch
vertical scale, and 2i chains to one inch
horizontal scale. This diagram ia, therefore,
applicable to 40 feet to 1 inch vertical scale,
and 5 chains to 1 inch horizontal scale. But,
owing to the fineness of the graduations, I
would not advise, to insure accuracy, that
the vertical scale be made less than 40 feet
to 1 inch, and, generally, the lai^er the
better. 20 feet to 1 inch vertical is a good
working scale. The lengtlis can be made
to suit c
There is no necessity to measure the heights or lengths
previously, and the same form must be used as before
described.
211
To Measure a Cutting by the Scale.
Apply the zero of the scale of aectional areas vertically to
the gradient or fonnation lincj and read off where the sunace
line intersects ; put this in column I or 3, as the case
requires : then, at the smaller end of the priamoid, upon
the scale of vCTtical yards, with lero on the surface hue,
observe where the gradient intersects, then place the same
point of intersection on the gradient at the other end, and
read off above the zero on the scale of differential areas,
where the surface line interaects ; put this in column 4, and
then, having measured all the lengths by the scale of
horizontal yards, proceed as in the use of the tables. To
save time, it is desirable to take a pair of dividers, and
mark off at each diviaiou the difference of the heights in
succession, and then the differential scale above zero need
only be applied.
This method of computing cubic contents of cuttings
and embankments is very expeditious vrith a little practice,
and is quite as accurate, and generally more so, than the
calculating by feet and the tables j because, in a working
section, the points of intersection of the scale and surface
line can be estimated readily by the eye ; but, in using an
ordinary scale of equal parts, we are compelled to neglect
the fractional parts of a foot. Should any of my refers
wish to obtain these scales, they can easily be made, by
giving a reasonable notice to Mr. Elliott, High Holbom.
the rule for forming them is as follows : —
To Calculate the Sectional Areas.
The formula is M'ea = g '^ ^i therefore, wlien
the area is graduated 10, 20, 30, 40, &e., in even
aion, we have 11=+ ^ H = 2 A j and the corre
hei^tisH=^2A + ^— fs;^^«^^ = 34-
212
'^^^ A ^ 34^
in yards, and « =3 to 1, the rule becomes H = 2A+--i^^ —
J 3 f 3*X4>«4
— 3t|t^ =^^"' (?)'—¥• To find the limit of the
graduation^ (a) the greatest height the scale may be
wanted for must be determined. The scale of differen-
tial areas is computed from the formula D = -g— ; therefore
the differences being graduated 1^ 2, B, 4^ &c.; 10^ 20^ 30^
&c. seriatim^ we have the corresponding height, H = ^^,
If required for slope 2 to 1, the rule becomes 1.728 VS.
From the preceding explanation it is evident that the
particular vertical scale being determined, a set of scales
for any number of bases can be easily made, as the only
variable portion is that of the sectional areas. These scales
are very convenient and portable, and can be frequently
employed in the absence of tables, by being carried in the
pocket, enclosed in a case.
(214)
AREAS OF LAND
FOR CUrriNGS AND EMBANK-
MENTS.
SLOPE f to 1.
SLOPE 1 to 1.
Ht.
Sides.
Ht.
Sides.
Ht.
Sides.
Ut.
Sides.
1
0000172
31
0005337
1
0000229
31
0007116
2 10000345
32
0005510
2
0000459
32
0007346
3
0000518
33
0005682
3
0000689
33
0007576
4
0000689
34
0005854
4
0000918
34
0007805
5
bo00861
35
0006026
5
0001148
36
0008036
6
b001033
36
0006198
6
0001377
36
0008264
7
0001205
37
0006371
7
0001607
37
0008494
8
0001377
38
0006542
8
0001836
38
0008723
9
0001550
39
0006714
9
0002066
39
0008953
10
0001722
40
0006887
10
0002296
40
0009182
11
0001893
41
0007059
11
0002624
41
0009411
12
0002066
ASt
0007231
12
0002754
42
0009641
13
0002238
43
0007403
13
0002984
43
0009871
14
0002410
44
0007575
14
0003213
44
0010100
15
0002586
45
0007748
16
0003443
46
0010330
16
0002755
46
0007920
16
0003673
46
0010569
17
0002927
47
0008093
17
0003902
47
0010789
18
0003099
48
0008265
18
0004132
48
0011018
19
0003272
49
0008436
19
0004361
49
0011248
20
0003444
50
0008608
20
0004591
50
0011478
21
0003615
51
0008781
21
0004820
51
0011707
22
0003788
52
0008953
22
0005060
52
0011937
23
0008960,
53
0009125
23
0005280
53
0012167
24
0004132
54
0009297
24
0005509
54
0012396
25
0004304
55
0009469
25
0005739
66
0012626
26
0004476
56
0009642
26
0006968
56
0012866
27
0004649
57
0009813
27
0006198
57
0013085
28
0004821
58
0009986
28
0006427
58
0013314
29
00G4992
59
0010158
29
0006667
59
0013644
30
0005165
60
0010331
30
0006887
60
0018774
(215)
AREAS OF LAND FOR CUTTINGS AND EMBANK-
MENTS.
SLOPE 1^ to
1.
SLOPE H to 1.
Ht.
Sides.
Ht.
Sides.
Ht.
Sides.
Ht.
Sides.
1
0000287
31
0008895
1
0000345
31
0010674
2
0000574
32
0009182
2
0000689
32
0011019
3
0000861
33
0009469
3
0001033
33
0011363
4
0001148
34
0009756
4
0001377
34
0011707
5
0001435
35
0010043
5
0001722
35
0012052
6
0001722
36
0010330
6
0002066
36
0012396
7
0002009
37
0010617
7
0002410
37
0012740
8
0002296
38
0010904
8
0002776
38
0013085
9
0002583
39
0011191
9
0003099
39
0013429
10
0002869
40
0011478
10
0003445
40
0013774
11
0003156
41
0011765
11
0003788
41
0014118
12
0003443
42
0012052
12
0004132
42
0014463
13
0003733
43
0012339
13
0004476
43
0014807
14
0004017
44
0012626
14
0004821
44
0015161
15
0004304
45
0012913
15
0005165
45
0015496
16
0004591
46
0013200
16
0005510
46
0015840
17
0004878
47
0013487
17
0005864
47
0016164
18
0005165
48
0013774
18
0006198
48
0016529
19
0005452
49
0014061
19
0006542
49
0016873
20
0005739
50
0014348
20
0006887
60
0017217
21
0006026
51
0014635
21
0007231
51
0017561
22
0006313
52
0014922
22
0007676
52
0017906
23
0006600
53
0015209
23
0007920
53
0016250
24
0006887
54
0015496
24
0008265
54
0018694
25
0007174
55
0015783
25
0006608
55
0018939
26
0007461
56
0016070
26
0008963
56
0019283
27
0007748
57
0016367
27
0009297
67
0019627
28
0008035
58
0016644
28
0009642
58
0019972
29
0008322
59
0016931
29
0009985
69
60
0020316
30
0008606
60
0017217
30
0000330
0020661
(216)
ACRES OF LAND FOR CUTTINGS AND EMBANK.
MENTS.
SLOPE If to 1.
SLOPE 2 to 1.
Ht.
Sides.
Ht.
SidM.
Ht.
Sides.
Ht.
Sides.
1
0000401
31
0012463
1
0000469
31
001^233
2
0000804
32
0012866
2
0000918
32
0014692
8
0001207
33
0013268
3
0001377
33
0016161
4
0001607
34
0013669
4
0001836
34
0016610
5
0002009
36
0014061
6
0002295
36
0016070
6
0002410
36
0014462
6
0002766
36
0016629
7
0002812
37
0014866
7
0003214
37
0016988
8
0003213
38
0016266
8
0003673
38
0017447
9
0003616
39
0016667
9
0004132
39
0017906
10
0004017
40
0016069
10
0004691
40
0018366
11
0004417
41
0016470
11
0006060
41
0018824
12
0004820
42
0016872
12
0005609
42
0019283
13
0006222
43
0017274
13
0006968
43
00197^
14
0005623
44
0017676
14
0006^27
44
0020201
16
0006026
46
0018078
16
0006887
46
0020661
16
0006428
46
0018479
16
0007346
46
0021120
17
0006829
47
0018882
17
0007805
47
0021679
18
0007231
48
0019283
18
0008264
48
0022038
19
0007633
49
0019684
19
0008723
49
0022497
20
0008035
60
0020086
20
0009183
60
0022966
21
0008435
61
0020488
21
0009641
61
0023416
22
0008838
62
00-20890
22
0010100
62
0023874
23
0009240
63
0021292
23
0010559
63
0024333
24
0009641
64
0021693
24
0011018,
54
0024792
26
0010043
66
0022095
26
0011478
66
0026262
26
0010444
66
0022497
26
0011937
66
0026711
27
0010847
67
002289ft
27
0012396
67
0026170
28
0011248
68
0023299
28
0012865
68
0026329
29
0011649
69
0023702
29
0013314
69
60
0027088
30
0012052
60
0024105
30
0013774
0027648
(217)
AREAS OF LAND FOR CU'lTINGS AND EMBANK-
MENTS.
•
SLOPE 2i to 1.
SLOPE 3 to 1.
Ht.
Sides.
Ht
Sides.
Ht.
Sides.
Ht.
Sides.
1
0000574
31
0017790
1
0000690
31
0021348
2
0001148
32
0018364
2
0001378
32
0022038
3
0001722
33
0018938
3
0002066
33
0022726
4
0002296
34
0019512
4
0002764
34
0023414
5
0002870
35
0020086
5
0003444
35
0024104
6
0003444
36
0020660
6
0004132
36
0024792
7
0004018
37
0021234
7
0004820
37
0026480
8
0004592
38
0021808
8
0005511
38
0026170
9
0005166
39
0022382
9
0006200
39
0026858
10
0005738
40
0022956
10
0006890
40
0027548
11
0006312
41
0023530
11
0007576
41
0028236
12
0006886
42
0024104
12
0008264
42
0028926
13
0007460
43
0024678
13
0008952
43
0029614
14
0008034
44
0025252
14
00096^
44
0030302
15
0008608
45
0025826
15
0010330
46
0030992
16
0009182
46
0026400
16
0011020
46
0031680
17
0009756
47
0026974
17
0011708
47
0032368
18
0010330
48
0027548
18
0012396
48
0033058
19
0010904
49
0028122
19
0013084
49
0033746
20
0011478
50
0028696
20
0013774
50
0034434
21
0012052
51
0029270
21
0014462
51
0035122
22
0012626
52
0029844
22
0015150
52
0036812
23
0013200
53
0030418
23
0016840
53
0036500
24
0013774
54
0030992
24
0016530
64
0037188
25
0014348
55
0031666
25
0017216
55
0037878
26
0014922
56
0032140
26
0017906
56
0038666
27
0016496
57
0032714
27
0018594
67
0039254
28
0016070
58
0033288
28
0019284
68
0039944
29
0016644
59
0033862
29
0019970
59
0040632
30
0017216
60 0034434
30
0020660
60
0041322
cc
(218)
Table for Estmating the Superficial Quantity
of Slrnaa of
Cuttings and Embankments in Rods,
SLOPE i to 1.
SLOPE i to 1.
Ht
CoBtenti
Ht
Contents
Ht.
1
Contents
Ht
Contents
A All*
in Rodt.
m*
inRoda.
in Rods.
XI b.
in Rods.
1
008786
81
117370
004106
81
127305
2
007572
32
121166
2
008213
32
131412
8
011358
33
12494'i
3
012320
38
135519
4
016144
34
128728
4
016426
34
139626
6
018931
85
132515
5
020533
35
143732
6
022717
36
136301
6
024640
36
147839
7
026503
37
140087
7
028746
37
161945
8
030289
38
143873
8
032863
38
166052
9
084075
39
147689
9
036960
39
160159
10
087861
40
161445
10
041066
40
164266
11
041647
41
166231
11
045172
41
168372
12
045433
42
169017
12
049279
42
172479
IS
049219
43
162803
13
053386
43
176686
14
053005
44
166689
14
057492
44
180692
15
066792
45
170376
16
061699
45
184799
16
060578
46
174162
16
066706
46
188906
17
064364
47
177948
17
069812
47
193012
18
068160
48
181734
18
073919
48
197119
19
071936
49
186520
19
078026
49
201226
20
075723
50
189307
20
082133
60
206332
21
079509
61
193093
21
086239
51
209438
22
083295
52
196879
22
090346
52
213645
23
087081
53
200665
23
094453
63
217652
24
090867
54
204461
24
0986^
64
221768
25
094654
65
208238
26
102666
56
225865
26
098440
56
212024
26
106773
66
229972
27
102226
67
215810
27
110879
57
234078
28
106012
68
219596
28
11^86
58
238185
29
109798
59
223382
29
119063
59
242292
30
113684
60 227168
30
123199
60
246399
(219)
Tabk for Estimating the Superficial QHantity of Slopes of
Cuttings and Embankments in Rods.
Ht.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
16
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
SLOPE } to 1.
I
SLOPE 1 to 1.
Contents
in Rods.
004591
009183
013774
018365
022957
027548
032139
036731
041322
045914
050505
055097
059688
064279
068871
073462
078053
082645
087236
091827
096418
101010
105601
110192
114784
119375
123966
128558
133149
137741
12^^ Contents
in Rods.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
66
66
61
58
59
60
142332
146924
151515
1561061
160698
165289
169880
174472
179063
183665
188246
192838
197429
202020
206612
211203
215794
220386
224977
229568
234159
238751
243342
247933
252525
257116
261707
266299
270890
275482
Ht.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Contents
in Rods.
005194
010389
015684
020778
025973
031167
036362
041556
046751
051945
057139
062334
067529
072723
077918
083112
088307
093501
098696
103891
109085
114280
119475
124669
129864
135058
140253
145447
150642
155836;
Ht.
Contents
in Rods.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
6^
61^
61
58
59
60
cc2
161030
166225
171420
176614
181809
187003
192198
197392
202587
207782
212976
218171
223366
228560
233755
238949
244144
249338
254533
259727
264921
270116
275311
280505
285700
290894
296089
301283
306478
311672
(220)
Table for Estimating the Superficial Quantity of Slopes of
Cuttings and Embankments in Rods,
SLOPE U to 1.
SLOPE 1) to
1.
Ht
Contents
Ht.
Contents
Ht
Contents
Ht
Contents
XA !»•
inRodi.
AA V*
in Rods.
AA«»
in Rods.
JLXw*
in Rods.
1
005880
31
182276
1
006^22
31
205275
2
011760
32
188165
2
013243
32
211896
3
017639
33
194034
3
919865
33
218518
4
023519
34
199914
4
026487
34
226140
5
029399
35
205794
5
033109
36
231762
6
035279
36
211674
6
039731
36
238384
7
041139
37
217634
7
046362
37
246005
8
047039
38
223434
8
052974
38
251627
9
052918
39
229313
9
059696
39
268249
10
058798
40
236193
10
066218
40
264871
11
064678
41
241073
11
072840
41
271493
12
070558
42
246963
12
079461
42
278114
13
076437
43
262832
13
086083
43
284736
14
082317
44
268712
14
092706
44
291368
15
088197
46
264592
16
099327
45
297980
16
094077
46
270472
16
106949
46
304602
17
099937
47
276332
17
112570
47
311223
18
105837
48
282232
18
119192
48
317845
19
111716
^
287111
19
126814
49
324467
20
117596
50
293991
20
132435
60
331088
21
123476
61
299871
21
139057
61
337710
22
129356
52
306751
22
145678
52
344331
23
135235
63
311630
23
162300
63
360953
24
141115
64
317610
24
158922
54
367676
26
146995
55
323390
26
165544
56
364197
26
152875
56
329270
26
172166
66
370819
27
168735
67
336130
27
178787
67
377440
28
164635
58
341030
28
185409
68
384062
29
170515
59
346909
29
192031
69
390684
30
176395
60
352789
30
198653
60
397306
(221)
Table for Estimating the Svperfiaial Qaantil^ qf Slopet of
SLOPE IJ to 1.
SLOPE 2 to 1. j
Ht
CoDtents jjt
Contents
Contents
Contents
b Bods. "*■
inKotk.
■
in Boas.
in Bods.
1
007403 31
229504
1
008213
31
254612
2
014807 32
236908
2
016427
32
262825
3
022210
33
244311
3
024640
33
271039
4
029613
34
251714
4
032853
34
279252
S
037017
35
259118
5
041066
35
287465
6
044420
36
266521
6
049280
36
295679
7
051824
37
273925
7
057493
37
303892
8
059227
38
281328
8
065706
38
312105
9
066630
39
288731
9
073920
39
320319
10
074034
40
296134
10
082133
40
328532
11
081437
41
303637
11
090346
41
336745
12
088841
42
310941
12
098660
42
344959
13
096244
43
318344
13
106773
43
353172
U
103647
44
325747
14
114986
44
361385
15
111061
45
333151
15
123199
45
369598
16
118454
46
340654
16
131413
46
377812
17
125858
47
347968
17
139626
47
386025
18
133261
48
365361
18
147839
48
394238
10
140664
49
362764
19
156063
49
402462
20
148067
50
370168
20
164266
50
410664
21
156470
51
377571
21
172479
51
418877
22
162874
52
384975
22
180693
62
427091
28
170277
53
392378
23
188906
63
436304
24
177680
54
399781
24
197119
64
443517
25
185084
55
407183
25
205332
55
451730
26
192487
56
414588
26
213546
66
«99«l
27
199891
57
421992
27
221769
67
468ii»»
28
207294
58
429395
28
229972
68
29
214697
59
436798
29
238186
59
48^^^V
30
222101 60
444201
30
246399
60
_ji^
(222)
Table for Estitruiting the Superficial Quantity of Slopes of
Cuttings and Embankments in Rods,
1
Ht.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
23
29
30
SLOPB 2i to 1.
Coatents
in Rods.
Ht.
.ir4:ii
019780
029670
039560
049450
0S9341
069231
079121
089011
098901
108791
118681
128571
138461
148351
158242
168132
178022
187912
197802
207692
217582
227472
237362
247252
257143
267033
276923
286813
296703
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
67
68
69
60
Contents
in Rods.
306593
316483
326373
336263
346153
356044
365934
375824
385714
395604
405494
415384
425274
435164
445054
454945
464835
474725
484615
4945a5
504395
514285
524175
634065
543955
553846
563736
573626
583516
593406
SLOPE 3 to 1.
Ht.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Contents
in Rods.
011616
023232
034846
046464
058077
069696
081307
092929
104638
116163
127768
139384
151000
162614
174230
185845
197460 47
Ht.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
46
46
Contents
in Rods.
209076
2-20691
232307
243922
255538
267153
278768
290384
292000
313614
325230
336845
348460
48
49
60
61
52
63
64
55
66
67
58
69
60
860076
371691
383306
394921
406537
418162
429767
441383
463000
464614
476229
487845
499460
611076
622691
634306
646921
667637
669162
580767
692382
604000
615613
627228
638844
650469
682074
673690
686305
696921
EXPLANATION OF TABLES
Ftyr Calculating the Areas of Land required for a Railivay,
Having prepared a form similar to that required for the
earthwork, look in the tables for the given slope, opposite
the given heights at each end of the prismoid, in the
columns headed " sides ;" and also look in the columns
headed ''bases/' which corresponds with slope 1 to 1 of the
sides, for a number corresponding with the given base added
to the two widths on each side between the edge of the
slope at the surface of the ground, and the boundary
or fence line. These three numbers added together and
multiplied by the length will give the area in acres and
decimals : all dimensions are given in feet.
Example :
Slope 1 to 1 ; base 32 feet.
Side widths, 12 feet each.
Heights, 18 and 38 feet; length, 560 feet.
Col. 1 Opposite 18 we find - - .0004132
Sides./Opposite38wefind - - .0008723
bScs \ Opposite 32 + 12 + 12 = 56 we find .0012855
.0025710
Multiply by length = 560
1.4397600
A. R. P.
Answer 1 1 30
224
It is obvious that in any given railway, whose base
and side widths are determined, the third number (in this
case .0012855) is common to all the additions ; therefore^
this may be multiplied by the entire length at once, and
the sides computed and added to the result afterwards.
Moreover, the same as in the earthwork, one tabular
number is common to two adjoining plots. Much time
may be saved also, by adding mentally the two heights
together, and seeking, if the tables admit of it, the corres-
ponding tabular number ; for
Opposite 18 we find .0004132
Opposite 38 " .0008723
Their sum is 56 .0012855
and opposite 56 we find .0012855.
Table to find the Superficial Quantity of Slopes.
Add together the numbers opposite the given heights,
and multiply the sum by the length ; the product in the
area is rods and decimals.
Example : the heights and slopes as before :
Opposite 18 we find .093501
Opposite 38 " .197392
56 .290893
Multiply by length 560
RODS. YDS.
Answer 162 27 162.900080
Here again, the sum of the heights being taken = 66,
the corresponding number is .290893.
- — "
( 225 )
TABLE OF OFFSETS TO CURVES,
Calculated for Radius = 1000.
Tan.
Offsett.
Tan.
Offsett.
Taa.
CMbett
Tan.
Offiwtt.
1
.0006
31
.4806
61
1.8623
91
4.1492
2
.0020
32
.5121
62
1.9239
92
4.2411
3
.0045
33
.5446
63
1.9865
93
4.3340
4
.0080
34
.5781
64
2.0501
94
4.4279
5
.0125
35
.6127
65
2.1148
95
4.6228
6
.0180
36
.6482
66
2.1804
96
4.6187
7
.0245
37
.6847
67
2.2471
97
4.7157
8
.0320
38
.7222
68
2.3147
98
4.8136
9
.0406
39
.7607
69
2.3833
99
4.9216
10
.0501
40
.8003
70
2.4530
100
5.0126
11
.0606
41
.8408
71
2.6237
101
5.1136
12
.0721
42
.8824
72
2.6954
102
5.2167
13
.0846
43
.9249
73
2.6681
103
5.3187
14
.0981
44
.9685
74
2.7418
104
6.4228
15
.1126
45
1.0131
75
2.8165
105
6.5278
16
.1281
46
1.0586
76
2.8922
106
5.6339
17
.1446
47
1.1052
77
2.9689
107
5.7411
18
.1621
48
1.1528
78
3.0466
108
6.8492
19
.1806
49
1.2013
79
3.1253
109
5.9584
20
.2001
50
1.2508
80
3.2052
110
6.0686
21
.2206
51
1.3013
81
3.2859
111
6.1796
22
.2421
52
1.3529
82
3.3677
112
6.2918
23
.2646
53
1.4054
83
3.4506
113
6.4061
24
.2881
54
1.4590
84
3.6343
114
6.5193
25
.3126
55
1.5137
85
3.6191
115
6.6346
26
.3381
56
1.5693
86
3.7049
116
6.7608
27
.3646
57
1.6259
87
3.7917
117
6.8681
28
.3921
58
1.6835
88
3.8795
118
6.9865
29
.4206
59
1.7421
89
3.9684
119
7.1068
30
.4501
60
L8017
90
4.0638
120
7.2262
:l.v
(226)
TABLE OF OFFSETS TO CURVES,
Calculated for Radius = 1000.
Tin.
OfEKtt.
Tan.
Offtett.
Tan.
Offfett.
Tan.
Offiwtt.
121
7.3474
151
11.4661
181
16.5168
211
22.5139
122
7.4797
152
11.6193
182
16.7013
212
22.7303
123
7.5931
153
11.7786
183
16.8869
213
22.9479
124
7.7176
154
11,9290
184
17.0736
214
23.1665
125
7.8433
156
12.0856
185
17.2615
215
23.3860
126
7.9696
166
12.2428
186
17.4502
216
23.6066
127
8.0971
167
12.4013
187
17.6400
217
23.8283
128
8.2276
168
12.5609
188
17.8310
218
24.0511
129
8.3572
160
12.7213
189
18.0229
219
24.2761
130
8.4861
160
12.8830
190
18.2160
220
24.5002
131
8.6175
161
13.0455
191
18.4099
221
24.7262
132
8.7501
162
13.2091
192
18.6050
222
24.9583
133
8.8837
163
13.3739
193
18.8012
223
25.1815
134
9.0185
164
18.5396
194
18.9986
224
25.4108
135
9.1544
165
13.7065
195
19.1968
225
25.6413
136
9.2910
166
13.8742
196
19.3960
226
25.8727
137
9.^87
167
14.0480
197
19.5964
227
26.1052
138
9.5675
168
14.2130
198
19.7978
228
26.3388
139
9.7074
169
14.3839
199
20.0004
229
2a5735
140
9.8485
170
14.5560
200
20.2041
230
26.8094
141
9.9903
171
14.7290
201
20.4087
231
27.0463
142
10.1332
172
14.9080
202
20.6144
232
27.2842
143
10.2772
173
15.0782
203
20.8212
233
27.5233
144
10.^23
174
16.2545
204
21.0291
234
27.7634
145
10.5685
175
15.4318
205
21.2381
235
28.0047
146
10.7154
176
15.6099
206
21.4480
236
28.2470
147
10.8684
177
15.7891
207
21.6590
237
28.4904
148
110126
178
16.9694
206
21.8711
238
28.7Md
149
11.1687
179
16.1508
209
22.0843
239
28.9805
150
-
11.3140
180
16.3334
210
22.2987
240 29.2271
(227)
TABLE OF OFFSETS TO CURVES,
Calculated for Radius = 1000.
Tan.
241
242
243
244
245
246
247
248
249
250
251
252
253
254
266
256
267
258
259
260
261
262
263
264
265
266
267
268
260
270
Offsett.
29.4746
29.7234
29.9734
30.2246
30.4770
30.7300
30.9842
31.2396
31.4963
31.7542
32.0126
32.2722
271
272
273
274
275
276
277
278
279
280
281
282
32.5331 283
:
32,7952
33.0686
33.3226
33.6880 287
33.8546 288
34.1225 289
34.3914 290
34.6610 291
34.9319 292
35.2039 293
35.4772 294
35.7516 295
36.0268 296
36.3032 297
36.6809 298
36.8597 299
37.1397 300
Tan.
284
286
286
Offsett.
37.4206
37.7026
37.9867
38.2701
38.5568
38.8422
39.1298
39.4186
39.7086
40.0000
40.2921
40.5864
40.8799
41.1766
41.4726
41.
42,0692
42.3694
42.6708
42.9734
43.2768
43.5815
43.8874
44.1946
44.5028
44.8120
45.1224
46.4340
46.7468
46.0608
Tan.
301
302
303
304
306
306
307
308
309
310
311
312
313
314
315
7702 316
317
318
319
320
321
322
323
824
325
326
327
328
329
330
Offsett.
46.3757
46.6919
47.0093
47.3279
47.6477
47.9684
48.2903
48.6135
48.9379
49.2635
49.5900
49.9178
50.2468
60.5770
60.9084
51.2408
51.5744
51.9092
52.2453
52.5825
52.9208
53.2603
63.6010
53.9429
64.2860
54.6302
54.9756
56.3223
55,6701
56.0191
Tan.
331
332
333
334
335
336
337
338
339
340
341
342
343
344
346
346
347
348
349
350
351
352
353
354
356
356
367
368
368
360
Offsett.
56.3692
56.7206
57.0732
57.4270
57.7819
68.1380
58.4954
58.8539
59.2137
59.5746
59.9367
60.3001
60.6646
61.0304
61.3973
61.7656
^.1349
62,6056
62.8773
63.2603
63.6246
64.0000
64.3767
64.7546
66.1337
66.5141
66.8957
66.2785
66.6625
67.0477
i
EXPLANATION
OF THE
TABLES OF OFFSETS TO CURVES.
In setting out the curves of a railway in the fields, the
usual practice is to lay out a tangent Ime, and from cer-
tain points along this line to set off at right angles such
distances as will give points in the curve : each distance is
called "an offset/* It has generally been considered suflBi-
cient, in setting out these curves, to calculate the offsets for
every chain of tangent, to the extreme length of 10 chains;
and the ordinary rule for this purpose (which is sufficiently
near when the radius is not less than two miles) is to com-
pute the extreme or last offset correctly^ and then all the
others are derived from it, by making the offsets vary as the
square of the tangent. But as the radius must be deter*
mined for every set, and therefore the application of a
table so constructed would be limited to a few given cases
only, I thought it better to provide such a table as would
be applicable to all cases, whether the radius were long or
short ; and the tangent might bear such a proportion to
the radius as would admit of the tables being used in
very sharp curves. For instance, in a curve of 10 chains
radius^ the tables wiU extend to 3.6 chains of tangent.
/
/
239
I now proceed to shew how these tables were formed,
I i 6 I S ^'"^ ^^^^ ^° explain their use.
Let AcC (in the accompanying
diagram) be the arc of a circle
required to be laid down ; AD is
cthe radius, AB the tangent, and
BC the offset. Abo Ac £c are
intermediate offsets. AC is the
chord. By the well known equa-
tion of a circle we hav e this rule to
findBC. BC=AI>— VaD* — AB'.
Suppose that AD were 1000, and
that tangents were given in the
ZJ series 1, 3, 8, 4, &c., corresponding
to A J, Ai, &c., then the offsets .0005, .0030, .0045, .0080,
&c., are the true distances be be, kc.
In the tables, every consecutive fifth number was calcu-
lated according to the above rule ; and the intermediate
numbers were interpolated. The error {if any) is m the
4th place of decimals only, and then not exceedmg any
where .0003; and this discrepancy, with a radius of 1000
chains, or 12j miles, will not equal j of an inch. There-
fore, the tables may be considered as practically accurate.
KDLB FOR THE TABLES.
Given radina and tangent, to find the offset. Divide
1 000 times the tangent by radius, and look in column of
t^gents for the quotient; then multiply the correspond,
ing opposite offset by 1,000 times the radius : the result is
the true offset.
= 50.
Radius, 3,940; tangent, 147. Here ^^^3^0°"
In the column of tangents in the tables we lot
and opposite to this, in the column of offset
1 2508 : this number multiplied by the rad
aiid divided by 1000, wiU pve the true offs
_ 1.2508 "2940 _ 8_677,
"" 1000
280
It is very easy to assume such a tangent as will give^
when divided, some nimiber to be found in the table;
which number should again admit of being sub-divided
into equal parts by some convenient divisor. For instance,
the above example (147) is easily divided by 2,940, and the
quotient 60 is found in the table. Also 50 can be divided
easily by 5 or 10, and will admit of 10 offsets 14.7 apart,
or 5 offsets 29.4 apart. In the first case, the numbers
opposite 5, 10, 15, &c., must be chosen to find the offsets;
and in the latter case, we should extract the numbers
opposite 10, 20, 30, &c. ; and computing these offsets as
b^ore, we can fill up so many points in the curve.
The use of these tables affords equal facility, whether
the calculations are made in feet, chains, yards, or any
other measure. Besides the use of computing the offsets
to curves, for small divisions on a tangent line, it is some-
times very desirable to know some remote point in a long
curve, for the purpose of checking the work, or when the
instruments for delineating curves are not long enough
to reach the whole extent of the required sweep. For
instance, in a working plan, plotted to 2^ chains to 1 inch,
or 32 inches to 1 mile, suppose a curve of 4 miles' radius
to extend over 2 miles of Ime, this will be 5 feet 4 inches
long ; and as the radius is 10 feet 8 inches, unless some
points were computed, it would not be safe to depend upon
the line which could be drawn by a sweep only 18 or 24
inches long. But, to make some of the points through which
the curve should pass, calculate them by the tables; thus:
Given radius 4 miles = 320 chains; tangents, 16,
32, 48, 64, 80 chains ; here, ?OjLl22? = 250 ; and as 250
divides easily by 5, we can extract the numbers opposite.
CHAINS.
250 = 31.7542^ then each f Offset for tangent 80
200 == 20.2041 number j '' '' 64
150 = 11.3140^ multiplied <{ '' '' 48
100 = 5.0126 1 by I '' '' 32
50 = 1.2508J 320-rl000l " " 16
231
It is now easy (having plotted these offsets) to join the
points by a proper sweep. To facilitate various calcula-
tions relating to curves, I subjoin the following rules : —
1. — Given tangent AB and offset BC ; to find radius
AD = AD :
AB^ + BC? Add together the squares of the tangent
2 BC and offset, and divide by twice the offset ; the
quotient is the radius.
2. — Given chord AC, and offset BC ; to find radius
AD = AD :
AC^ Divide the square of the chord by twice the
2 BC offset ; the quotient is the radius.
BC == 3. — Given radius and tangent ; to find the offset :
From the radius deduct the square root of
A D — the difference of the squares of the radius and
VAD^ AW tangent ; the result is the offset.
BC = 4. — Given the radius and chord ; to find the offset :
AC^ Divide the square of the chord by twice the
2 AD radius ; the quotient is the offset.
AB = 5. — Given the chord and offset ; to find the tangent.
VaC^— BC^ Take the square root of the difference of the
squares of the chord and offset ; the result is
the tangent.
AB = 6. — Given the radius and offset; to find the tangent:
V2 AD X BC Multiply the difference of twice the radius
— BC" and the offset by the offset ; and the square
root of the product is the tangent.
7. — Given the tangent and offset; to find the
AC = chord:
VaB^Tbc? Add together the squares of the tangent
and offset ; the square root of the sum is the
chord.
8. — Given the radius and offset; to find the
AC = chord :
V2 BC X AD Multiply twice the offset by the radius j the
square root of the product is the chord.
1
232
TMe for finding the Radius, when the Tangent is knoum,
and the AngU subtending the are is given (contained
between the two tangents to the extreme points of the arc).
'Rxiij&—To find the radius.
Multiply the tangent by the coefficient opposite the
given angle; the product is the radius.
Angle.
179i
179
1784
178
1774
177
176 J
176
175|
175
174*
174
173i
173
172i
172
171J
171
170i
170
169i
169
168}
168
167*
167
166*
166
165*
165
Coefficient.
229.18
114.60
76.40
57.30
45.84
38.20
32.74
28.65
25.47
22.92
20.84
19.10
17.64
16.38
15.29
14.33
13.49
12.74
12.07
11.47
10.92
10.43
9.981
9.567
91.85
8.833
8.507
8.205
7.924
7.661
II Angle.
Coefficient
164*
7.415
164
7.185
163j
6.969
163
6.765
162i
6.573
162
6.392
161*
6.221
161
6.059
leoj
5.905
160
5.758
159*
5.619
159
5.487
158*
5.361
158
5.241
157*
5.125
157
5.015
156i
4.910
156
4.809
155i
4.713
155
4.620
154i
4.531
154
4.445
153i
4^363
153
4.283
152i
4.207
152
4.133
151*
4.062
151
3.994
150j
3.927
150
3.863
233
Given radius and angle ; to find corresponding tangent.
Rule — ^Divide radius by coefficient due to the angle;
the quotient is the required tangent.
EXPLANATION OF THE TABLE OF DISTANCES.
For the convenience of those who wish to transfer chains
into feet or yards, or the reverse, I have supplied tables,
giving the comparative values of any desired distances at
once ; and by multiplying or dividing the numbers given
in the table by 10, it is easy to obtain any extension of the
tables required in practice.
B D
A
(234)
TABLE OF DISTANCES.
Chains into Yards and Feet.
Miles
Chains.
YariU.
Feet.
Miles
Chains.
Yards.
Feet.
.01
.22
.66
11
242
726
.02
.44
1.32
i 12
264
792
.03
.66
1.98
13
286
858
.04
.88
2.64
14
306
924
.05
1.10
3.30
,'<
16
330
990
.06
1.32
3.96
16
352
1056
.07
1.54
4.62
17
374
1122
.08
1.76
5.28
18
396
1188
.09
1.98
5.94
19
418
1254
.10
2.20
6.60
i
20
440
1320
.20
4.40
13.20
21
462
1386
.30
6.60
19.80
22
484
1452
.40
8.80
26.40
23
506
1518
.50
11.00
33.00
24
528
1584
.60
13.20
39.60
6
16
25
550
1650
.70
15.40
46.20
26
572
1716
.80
17.60
52.80
27
594
1782
.90
19.80
59.40
28
616
1848
1.00
22.00
66.00
29
638
1914
2.00
44.00
132.00
1
30
660
1980
3.00
66.00
198.00
31
682
2046
4.00
88.00
264.00
32
704
2112
5.00
110.00
330.00
33
726
2178
1
u
6.00
132.00
396.00
34
748
2244
7.00
154.00
462.00
7
16
35
770
2310
8.00
176.00
528.00
36
792
2376
9.00
198.00
594.00
37
814
2442
i
10.00
220.00
660.00
38
39
836
858
2508
2574
h
40
880
2640
I
I
1
(235)
TABLE
. OF DISTANCES. 1
Chains into Yards and Feet.
— — — >^ 1
Miles
Yard*.
Feet.
Mileg
Clwiiii.
Yard*.
Feet
41
902
2704
71
1662
4686
42
924
2772
1 72
1584
4762
43
946
2838
1 73
1606
4818
44
968
2904
74
1628
4884
9
16
45
990
2970
ij ; 76
1660
4950
46
1012
3036
76
1672
6016
47
1034
3102
, 77
1694
6082
48
1056
3168
i 78
1716
6148
49
1078
3234
79
1738
5214
1
50
1100
3300
1 80
1760
5280
51
1122
3366
81
1782
5346
52
1144
3432
i 82
1804
5412
53
1166
3498
; 83
1826
6478
54
1188
3564
84
1848
6544
11
16
55
1210
3630
1.', 85
1870
5610
56
1232
3696
86
1892
5676
57
1254
3762
1 87
1914
6742
58
1276
3828
88
1936
5808
59
1298
3894
89
1958
6874
1
60
1320
3960
U
90
1980
5940
61
1342
4026
91
2002
6006
62
1364
4092
92
2024
6072
63
1386
4158
93
2046
6138
64
1408
4224
94
2068
6204
13
16
65
1430
4290
1?,
95
2090
6270
66
1462
4356
96
2112
6336
67
1474
4422
97
2134
6402
68
.1496
4488
98
2156
6468
69
1518
4554
99
2178
6534
i
70
1540
4620
u
100
2200
6600
D d2
j
I
J
(£36)
TABLE
OF DISTANCES.
Chains into Yards and Feet.
Mile*
Chains.
Yards.
7«et.
Miles
41
Chains.
Yards.
Jrcct*
1.'.
105
2310
6930
350
7700
23100
li
110
2420
7260
4i
360
7920
23760
17.
115
2630
7590
4*
370
8140
24420
li
120
2640
7920
4i
380
8360
25080
U
125
2750
8260
45
390
8680
25740
1*
130
2860
8680
5
400
8800
26400
US
ia5
2970
8910
6J
410
9020
27060
11
140
3080
9240
6i
420
9240
27720
Hi
146
3190
9570
51
430
9460
28380
IJ
1-50
3300
9900
5i
440
9680
29040
115
•••18
156
3410
10230
51
450
9900
29700
2
160
3620
10560
4i
460
10120
30360
2i
170
3740
11220
51
470
10340
31020
2i
180
3960
11880
6
480
10560
31680
21
190
4180
12540
6t
490
10780
32340
2i
200
4400
13200
6i
600
11000
33000
2f
210
4620
13860
61
610
11220'
33660
2i
220
4840
14520
6i
520
11440
34320
2i
230
5060
15180
61
630
11660
34980
3
240
5280
16840
6i
540
11880
a5640
3i
250
5600
16500
6J
560
12100
36300
3i
260
5720
17160
7
560
12320
36960
31
270
6940
(7820
7J
570
12540
37620
3i
280
6160
18480
7J
580
12760
38280
31
290
6380
19140
71
690
12980
38940
3i
300
6600
19800
7i
600
13200
39600
3J
310
6820
20460
7f
610
13420
40260
4
320
7040
21120
71
620
13640
40920
4J
330
7260
21780
75
630
13860
41580
4i
340
7480
22440
8
640
14080
42240
' 237 ■
TABLE OF DISTANCES.
Yards inia Cbams aad Feet.
Feet.
Ta^.
o^
Fort.
Tardk
1**^
.1
.0^
-CBllo *
21
, 7-000
.3181
51
.006
/-■>30
-22
, 7.333
.3333
^
.100
■ .Ci>4o
23
7.666
.3184
A
.133
.^JiJdiJ
21
8.000
.3636
.5
.166
-tJjTo
25
8.3^
.3787
.6
J200
-OiJOO
26
8.666
.3939
.7
.233
.0106
27
9.000
.4090
^
J266
-0121 •
28
9.333
.ASASt
.9
.300 '
.0136 i
29
9.666
.4393
1.0
.333
.0151 !
30
lO.OOO
.4545
2.0
.oob
.0303
31
10.333
.4696
3.0
1.000
.0154
32
10.666
.4848
4.0
1.333
.0606
33
11.000
.5000
5.0
1.666
.0757
34
11.333
.5151
6.0
2.000
.0909
35
11.666
.5303
7.0
2.333
.1060
36
12.000
.5454
8.0
2.666
.1212
37
12.333
.5606
9.0
3.000
.1363
38
12.666
.5757
10.0
3.333
.1515
39
13.000
.5909
11.0
3.666
.1666
40
13.333
.6060
12.0
4.000
.1818
41
13.666
.6212
13.0
4.333
.1969
42
14000
.6363
14.0
4.666
.2121
43
14.333
.6515
15.0
5.000
.2272
44
14.666
.6666
16.0
5.333
.2421
45
15.000
.6818
17.0
5.666
.2575
46
15.333
.6969
18.0
6.000
.2727
47
15.666
.7121
19.0
6.330
.2878
48
16.000
.7272
20.0
6.666
.3030
49
16.333
.7424
50
16.C6(i
.7676
11
|l
(238)
TABLE OF DISTANCES.
Feet into Chaing and Yards.
Yards.
Feet.
Chung.
Yards.
Feet*
Chains.
.1
.8
.0045
21
63
.9545
.2
.6
.0090
22
66
1.0000
.8
.9
.0136
23
69
1.0464
.4
1.2
.0181
24
72
1.0909
.6
1.6
.0227
26
75
1.1363
.6
1.8
.0272
26
78
1.1818
.7
2.1
.0318
27
81
1.2272
.8
2.4
.0363
28
84
1.2727
.9
2.7
.0409
29
87
1.3181
1.0
8.0
.0454
30
90
1.3636
2.0
6.0
.0909
81
98
1.4090
3.0
9.0
.1363
32
96
1.4545
4.0
12.0
.1818
33
99
1.5000
5.0
15.0
.2272
34
102
1.6464
6.0
18.0
.2727
35
105
1.5909
7.0
21.0
.3181
36
108
1.6363
8,0
24.0
.3636
37
111
1.6818
9.0
27.0
.4090
38
114
1.7272
10.0
30.0
.4546
39
117
1.7727
11.0
33.0
.5000
40
120
1.8181
12.0
36.0
.6454
41
128
1.8636
13.0
39.0
.5909
42
126
1.9090
14.0
42.0
.6363
43
129
1.9645
15.0
45.0
.6818
44
132
2.0000
16.0
48.0
.7272
45
135
2.0464
17.0
51.0
.7727
46
138
2.0909
18.0
64.0
.8181
47
141
2.1363
19.0
57.0
.8636
48
144
2.1818
20.0
60.0
.9090
49
147
2.2272
60
150
2.2727
(289)
1
1
TABLE OP GRADIENTS.
1
•S-S
Vert, alt
. Vert, alt
. Gravity in
cTS
Vert alt.
Vert. alt.
Gnu in
4 S
in feet
in feet
lb«. due
•|»
in feet
in feet
lbs. dne
e3§
22
per mile
, perchaii
1 to I ton.
i2§
52
per mile.
perchaii
to 1 ton.
240.0C
1 3.000C
1101.816
101.53
1.2692
43.076
23
229.56
2.8696
97.368
53
99.62
1.2462
42.264
24
220.00
2.7500
93.336
54
97.77
1.2222
41.480
25
211-20
2.6400
89.600
55
96.00
1.2000
40.726
26
203.06
2.5384
86.152
56
94.28
1.1786
40.000
27
195-55
2.4444
82.960
57
92.63
1.1578
39.298
28
188.56
2.3572
80.000
58
91.03
1.1377
38.620
29
182.06
2.2758
77.240
59
89.49
1.1186
37.966
30
176.00
2.2000
74.666
60
88.00
1.1000
37.333
31
170.32
2.1290
72.216
61
86.55
1.0818
36.720
32
165.00
2.0625
70.000
62
85.16
1.0645
36.108
33
160.00
2.0000
67.880
63
83.81
1.0477
35.555
34
155.30
1.9413
65.880
64
82.50
1.0312
35.000
35
150.84
1.8856
64.000
65
81.23
1.0152
34.460
36
146.66
1.8333
62.222
66
80.00
1.0000
33.940
37
142.70
1.7839
60.540
67
78.81
.9851
33.432
38
138.95
1.7368
58.944
68
77.64
.9706
32.940
39
135.38
1.6923
57.436
69
76.49
.9563
32.464
40
132.00
1.6500
56.000
70
75.43
.9429
32.000
41
128.78
1.6098
54.634
71
74.36
.9296
31.660
42
125.71
1.5714
53.333
72
73.33
.9166
31.111
43
122.78
1.5348
52.092
73
72.32
.9041
30.685
44
120.00
1.5000
50.908
74
71.35
.8919
30.270
45
117.33
1.4666
49.777
75
70.40
.8800
29.867
46
115.04
1.4380
48.684
76
69.47
.8684
29.472
4
47
112.34
1.4042
47.660
77
68.57
.8570
29.090
■
48
110.00
1.3750
46.688
78
67.69
.8461
28.718
49
107.75
1.3470
45.716
79
66.83
.8355
28.355
60
105.60
1.3200
44.800
80
66.00
.8250
28.000
51 103.52
1.2941
43.920
81
65.20 1
.8140
27.718
(240)
TABLE OF GRADIENTS.
Ratio.
Ver.tl.
Ver.tl.
Ora. in
T% A •
Ver. al
Ver.al.
Gra. in
in feet
in feet
lbs. due
Ratio.
in feet
in feet
Ibi. due
One in
per m.
per ch.
to 1 ton.
One in
per m.
per ch.
to I ton.
82
64.39
.8048
27.317
no
48.00
.6000
20.363
83
63.61
.7952
26.988
111
47.57
.5940
20.180
84
62.86
.7857
26.666
112
47.14
.5893
20.000
85
62.12
.7764
26.353
113
46.72
.5840
19.823
85.16
62.00
.7750
26.303
114
46.31
.6789
19.649
86
61.39
.7674
26.046
115
45.93
.5739
19.478
87
60.69
.7586
25.746
116
45.52
.5688
19.310
88
60.00
.7500
25.454
117
45.13
.5641
19.145
89
59.33
.7416
25.168
118
44.75
.5593
18.983
90
68.66
.7333
24.888
119
44.37
.5545
18.820
91
58.02
.7252
24.614
120
44.00
.5500
18.666
92
57.62
.7190
24.342
121
43.64
.5464
18.512
93
56.77
.7096
24.086
122
43.28
.5409
18.360
94
56.17
.7021
23.830
123
42.92
.5364
18.210
95
55.60
.6900
23.679
124
42.58
.5322
18.054
96
55.00
.6875
23.334
125
42.24
.5280
17.920
97
54.43
.6804
23.092
126
41.90
.6238
17.777
98
53.88
.6735
22.858
127
41.57
.5196
17.638
99
53.33
.6666
22.626
128
41.26
.5157
17.500
100
52.80
.6600
22.400
128.78
41.00
.5126
17.394
101
52.27
.6535
22.180
129
40.93
.6016
17.364
102
51.76
.6470
21.960
130
40.61
.5076
17.230
103
61.26
.6408
21.747
131
40.08
.5009
17.099
104
50.77
.6346
21.538
132
40.00
.6000
16.970
105
50.28
.6285
21.333
133
39.70
.4962
16.842
105.6
50.00
.6250
21.212
134
39.40
.4926
16.716
106
49.81
.6226
21.132
135
39.11
.4888
16.692
107
49.34
.6168
20.934
136
38.82
.4853
16.470
108
48.89
.6111
20.740
137
38.64
.4816
16.360
109
48.44
.6056
20.655
138
38.24
.4782
16.232
I-
(241)
TABLE OF GRADIENTS.
Ratio.
Ver. al.
Ver. al.
Ora. in
^r« M.9
Ver.al.
Ver.al.
Gnu in
in feet
in feet
lbs. due
Ratio.
in feet
in feet
lbs. doe
One in
per m.
per ch.
to I ton.
One in
per m.
per ch.
to 1 ton.
139
38.00
.4750
16.114
168 '
31.43
.3929
13.333
140
37.71
.4713
16.000
169
31.24
.3904
13.254
141
37.44
.4680
15.886
170
31.06
.3883
13.176
142
37.18
.4648
15.775
171
30.88
.3869
13.099
143
36.92
.4614
15.666
172
30.69
.3837
13.023
144
36.66
.4583
15.555
173
30.57
.3821
12.942
145
36.41
.4551
15.448
174
30.34
.3793
12.873
146
36.16
.4520
15.342
175
30.17
.3771
12.800
147
35.92
.4489
15.238
176
30.00
.3760
12.727
148
35.67
.4459
15.135
177
29.83
.3729
12.666
149
35.44
.4426
15.033
178
29.66
.3708
12.684
150
35.20
.4400
14.933
179
29.50
.3687
12.514
150.85
35.00
.4375
14.849
180
29.33
.3666
12.444
151
34.97
.4371
14.834
181
29.17
.3646
12.376
152
34.74
.4341
14.736
182
29.01
.3626
12.307
153
34.44
.4305
14.640
182.07
29.00
.3625
12.306
154
34.28
.4285
14.545
183
28.85
.3606
12.240
155
34.06
.4257
14.452
184
28.76
.3695
12.171
156
33.84
.4230
14.359
185
28.54
.3567
12.108
157
33.62
.4203
14.268
186
28.39
.3548
12.043
158
33.42
.4177
14.177
187
28.24
.3529
11.980
159
33.21
.4150
14.088
188
28.08
.3511
11.916
160
33.00
.4125
14.000
188.5
28.00
.3500
11.883
161
32.80
.4088
13.912
189
27.93
.3429
11.852
162
32.60
.4070
13.859
190
27.80
.3466
11.789
163
32.39
.4048
13.741
191
27.65
.3456
11.727
164
32.19
.4024
13.668
192
27.50
.3437
11.667
165
32.00
.4000
13.576
193
27.36
.3420
11.606
166
31.81
.3976
13.494
194
27.22
.3402
11.646
167
31.62
.3952
13.41^
196
27.07
.3384
11.487
(242)
TABLE OF GRADIENTS.
•
Ver, dt.
Ver. alt
Gnu in
V^ . m
Ver. alt.
Vr.alt.
Gra. in
Katio.
in feet
in feet
lbs. doe
Ratio.
in feet
in feet
lbs. due
One in
per mile.
per cb.
to 1 ton.
One in
per mile.
perdi.
.2598
to 1 ton
196
26.938
.3367
11.429
254
20.787
8.819
198
26.666
.3333
11.313
256
20.625
.2578
8.760
199.25
26.50
.3312
11.242
260
20.30
.2537
8.615
200
26.40
.3300
11.200
264
20.00
.2500
8.485
203
26.00
.3250
11.034
266
19.85
.2481
8.421
204
25.882
.3235
10.980
268
19.701
.2462
8.358
205
25.756
.3219
10.927
270
19.55
.2444
8.296
206
25.631
.3204
10.873
270.77
19.50
.2437
8.273
207
25.507
.3188
10.821
272
19.411
.2426
8.235
208
26.38
.3173
10.769
274
19.270
.2408
8.175
210
25.14
.3142
10.666
275
19.20
.2400
8.146
211.2
25.00
.3125
10.606
276
19.17
.2396
8.116
212
24.905
.3113
10.666
278
19.00
.2375
8.057
216
24.44
.3055
10.370
280
18.85
.2366
8.000
220
24.00
.3000
10.181
282
18.72
.2340
7.943
224
23.571
.2946
10.000
285.4
18.60
.2312
7.849
225
23.47
.2934
9.955
286
18.461
.2307
7.832
226
23.362
.2920
9.911
288
18.33
.2291
7.777
228
23.158
.2895
9.824
290
18.20
.2276
7.724
229.5
23.00
.2875
9.760
292
18.08
.2260
7.671
230
22.95
.2868
9.739
293.3
18.00
.2250
7.637
232
22.758
.2844
9.655
296
17.838
.2229
7.567
236
22.373
.2796
9.491
300
17.60
.2200
7.466
240
22.00
.2750
9.333
301.71
17.50
.2187
7.424
242
21.82
.2727
9.256
306
17.22
.2152
7.320
245
21.55
.2693
9.143
310
17.03
.2128
7.226
246
21.46
.2682
9.105
310.6
17.00
.2125
7.212
250
21.12
.2640
8.960
314
16.812
.2101
7.134
251.4
21.00
.2625
8.910
315
16.76
.2095
7.111
262
20.952
.2619
8.888
318
16.603
.2076
7.044
(S4J)
ll
TABLE OF GRADIENTS.
lUtio.
TcT.i]t.lT<r..L'Gn.B
Vff. dt
V^..I.<G» i.
infcct jnfa4 iIlM.dw
^Bik.jMr<L|toItni
16.50 1.206? 7.000
BMio.
ikln
mkt
Ow-iIk
Om in
OMm
OTldk.
^^
mlm 1
320
t06.1
13.00
.1625
5.517 '
322
16.398.204+! 6.956
410
12.878
.1609
5.463
326
16.196.2024 6.871
415
12.722
.1590
5.397
330
16.00 .2000.6.787
420
12-57
.1571
5.333 ■
334
15.809.1976,6.706
15.621i .19521 6.627
122.4
12.50
.1562
5.303 1
338
425
12.42
.1553
5.230 1
340
15.53
.1941 6.58*
(30
12.28
.1535
5.209
344
15.34
.1917 6.511
435
12.13
.1517
5.149
348
15.122
.1896 6.436
440
12.00
.1500
5.090
350
15.08
.1885 6.400
445
11.865
.1483
5.033
352
15.00
.1875 6.363
449
11.76
.1470
4.989
356
14.831
.1854 6.292
450
11.73
.1466
4.977
360
14.666
.1833
6.222
455
11.626
.1453
4.923
362
14.589
.1823
6.188
459.13
11.50
.1437
4.879
364.13
14.60
.1812
6.152
(60
11.47
.1434
4.869
366
14.426
.1803
6.120
(65
11.35
.1419
4.817
370
14.27
.1783
6.054
(70
11.23
.1404
4.766
372
14.192
.1774
6.018
(75
11.12
.1380
4.716
375
14.08
.1760
5.973
(80
11.00
.1375
4.666
376
14.04
.1755
5.957
(84
10.909
.1363
4.628
377.1
14.00
.1750
5.941
(85.
10.886
.1361
4.616
380
13.90
.1737
5.894
(90
10.77
.134(
4.571
384
13.75
.1718
5.833
(95
10.666
4.525
388
13.608
.1701
5.773
500
10.56
1320
4.480
390
13.54
.1692
5.743
502.85
10.50
:i312
4.455
•Ifti 11
13.50
IA»7
.1797
=i05
10 4'i'^
1
(244)
TABLE OF GRADIENTS.
Ver. Alt.
Yr. ALIGrs. inl
V% M.9
Ver. Alt
Ver.Al.
6n.in
Ratio.
in feet
infect
ll».dae
Ratio.
in feet
in feet
lb8.diie
One in
per mile.
per di.
tolton
One in
per mile.
perch.
tolton
520
10.15
.1268
4.307
690
7.65
.0956
3.246
525
10.057
.1257
4.266
700
7.54
.0942
3.200
528
10.00
.1250
4.242
704
7.50
.0937
3.182
630
9.962
.1245
4.226
710
7.436
.0929
3.155
635 ^
9.86
.1233
4.187
720
7.33
.0916
3.111
540
9.77
.1222
4.148
730
7.23
.0905
3.068
545
9.689
.1211
4.110
740
7.13
.0891
3.027
550
9.60
.1200
4.072
750
7.04
.0880
2.986
555
9.513
.1189
4.036
754.3
7.00
.0875
2.970
555.68
9.50
.1187
4.031
760
6.947
.0868
2.947
560
9.42
.1178
4.000
763
6.92
.0865
2.935
565
9.345
.1168
3.964
770
6.857
.0857
2.909
570
9.266
.1150
3.929
780
6.77
.0846
2.871
575
9.182
.1145
3.895
790
6.685
.0835
2.835
580
9.103
.1138
3.862
800
6.60
.0825
2.800
586
9.02
.1128
3.829
810
6.518
.0814
2.765
686.6
9.00
.1125
3.818
812.3
6.50
.0812
2.758
590
8.949
.1118
3.796
820
6.439
.0805
2.731
595
8.874
.1109
3.764
830
6.36
.0795
2.698
600
8.800
.1100
3.733
840
6.285
.0785
2.666
610
8.655
.1082
3.672
850
6.21
.0776
2.635
620
8.516
.1064
3.611
860
6.139
.0767
2.604
621.17
8.50
.1062
3.606
870
6.06
.0758
2.574
625
8.48
.1056
3.584
880
6.00
.0750
2.545
630
8.38
.1047
3.555
890
5.932
.0741
2.516
640
8.25
.1031
3.500
900
5.86
.0733
2.488
650
8.123
.1015
3.446
910
5.802
.0725
2.461
660
8.00
.1000
3.393
920
5.739
.0717
2.434
670
7.880
.0985
3.343
930
5.67
.0709
2.408
680
7.76
.0970
3.294
940
5.617
.0702
2.383
«
(245)
TABLE OF GRADIENTS.
V^ J.*
Ver.Al.
Ver.Al.
6m. in
V^ . •
Vr.Al
Vr.Al.
Gnuin
Ratio.
in feet
in feet
lbs. doe
Ratio.
in fee
infbet
lbs. due
One in
per mile
perch.
to! ton
One in
per m
perch.
to 1 ton
950
5.55
.0694
2.357
1760
3.00
.0375
1.272
960
5.50
.0687
2.333
1800
2.933
.0366
1.244
970
5.443
.0680
2.309
1850
2.854
.0356
1.211
980
5.38
.0673
2.285
1900
2.780
.0345
1.178
1 990
5.333
.0666
2.262
1950
2.707
.0338
1.148
1000
5.280
.0660
2.240
2000
2.64
.0330
1.120
1050
5.028
.0628
2.133
2100
2.514
.0314
1.066
1056
5.00
.0625
2.121
2112
2.50
.0312
1.060
1100
4.80
.0600
2.036
2200
2.40
.0300
1.018
1150
4.591
.0574
1.947
2300
2.295
.0286
0.973
1173.33
4.50
.0562
1.909
2400
2.200
.0275
.933
1200
4.40
.0550
1.866
2500
2.112
.0264
.896
1234
4.2787
.0535
1.815
2600
2.030
.0253
.861
1250
4.224
.0528
1.792
2640
2.00
.0260
.848
1300
4.061
.0507
1.723
2700
1.955
.0244
.829
1320
4.00
.0500
1.697
2800
1.885
.0235
.800
1350
3.911
.0488
1.659
2870
1.84
.0230
.780
1400
3.77
.0471
1.600
2900
1.820
.0227
.772
1440
3.66
.0458
1.555
3000
1.760
.0220
.746
1450
3.641
.0455
1.544
3200
1.650
.0206
.700
1500
3.52
.0440
1.493
3400
1.553
.0194
.658
1508.57
3.50
.0437
1.485
3520
1.500
.0187
.636 1
1520
3.47
.0433
1.473
3600
1.466
.0183
.622
1550
3.406
.0425
1.445
3800
1.390
.0173
.589
1600
3.30
.0412
1.400
4000
1.320
.0165
.560
1620
3.26
.0407
1.382
4285
1.232
.0154
.522 :
1650
3.20
.0400
1.357
4500
1.173
.0146
.497
1700
3.106
.0388
1.317
5000
1.056
.0132
.448
1730
3.052
.0381
1.294
5280
1.000
.0125
.424
1750
3.017
.0377
1.280
J
EXPLANATION
OF TBI
USE OF THE TABLES OF GRADIENTS.
The first column gives the ratio of the horizontal length
to an nnit of vertical height^ as when in column 1 we find
160^ it signifies that the gradient indicated has one foot
vertical rise to 160 feet horizontal lengthy commonly writ-
ten ^^indination 1 in 160/' The second column gives
the number of feet of vertical rise per mile due to the incli-
nation indicated in column 1. The third column gives the
number of feet of vertical rise per chain due to the same in-
clination. The fourth column gives the number of poimds
avoirdupois required to be exerted by an engine to over-
come the gravitation of one ton weighty to be moved up-
wards along the same inclination.
To calculate the rise or fall of gradients^ multiply the
tabular number corresponding to the required chanu^er
opposite to the given inclination by the lengthy and the
product will give the total rise in feet. Example — Gra-
dient 1 in 160^ length 125 chains. Opposite 160 we find
.4125 j and .4125 x 125 = 51.56 feet vertical rise.
It is hardly necessary to observe that these tables ad-
mit of being applicable to gradients not contained therein,
by applying any required multiple — as 2, 8, 4, 5, &c., or
h if if h ^' — ^ some gradients included in the table.
For instance^ the rise due to 1 in 19 may be found by
doubling that of 1 in 38^ and the rise due to 1 in 4650
may be found by dividing that due to 465 by 10, or that
of 155 by 30, &c.
While plotting a series of gradients, I sfaoold sDggest
the following form of arranging them, as rendering the
calculations easier to be checked and to be referred to : —
LIST or GaADIBNTS,
_ at a point elevated {50) feet above the
line: —
Ineliiiatian.
DMdibc
whether
iMorfUl
r
otal length
terminiu.
Veit-tiM
Vert.Wl,
Nl
nLdlw. I
■Jlee
ehni.
feet.
feet.
fest.
1 in 160
rise
40
40
16.50
66.50
252
f«n
32
72
8.38
58.12
4801 fall
70
1
62
9,42
48.70
Level level
45
2
27
48.70
132 ri.e
62
3
9
31.00
79.70
4M rise
18
3
27
2.56
83.26
920 fall
1 11
4
38
6.52
75.74
100 Ml
28
4
66
1.85
78.89
264 rise
4«
5
82
11.50
85.39
Proof of Length | 5 82
61.56 1 26.17 1
26.17
Effective nse
35.89
Add terminnB above datum —
50.00
Proof ofl
leight
-
85.39
By computing the gradients from the total lengths, they
will be made to agree with the mileage. I recommend
that the gradients be estimated in feet and decimals, and
not in feet and inches, the decimal method being more
accurate.
The use of the fourth column in the table
described —
Suppose that it were required to know tli
influence of any incline on a railway — for exi
incline of 1 in 160 ; then in column four, <
we find 141bs, per ton; and if the load
248
(including the engine and tender) be 100 tons, then
100 X 14 = 14001bs. would represent the resistance to
motion upwards^ and also it would represent the force
assisting the train to descend the same gradient. It is
manifest that the forces up and down are in equilibrium ;
therefore any given incline will not, by itself, be a suffi-
cient datum to find the preponderating influence of the
whole series of inclines. By the term preponderance I
wish to express " the excess of force due to gravity alone,
with which the load drawn resists the tractive power, in
one direction, over that force which is similarly exerted
in the opposite direction.^^ As the resistance, due to
gravity, on an ascending gradient, is measured by the
height through which the load is raised ; and as the pro-
petting force, due to gravity, on a descending gradient, is
measured by the height through which the load is lowered;
it follows, that part of the force expended to raise the load
wiU be restored by the self-propelUng influence of gravity,
when the load shall begin to descend. If the descent is
greater than the ascent, there will be a surplus of gravi-
tating power, or the "preponderance" will be active in
the opposite direction to the given motion; but if the descent
is less than the ascent, there will remain a portion of the
tractive force unbalanced, or the ''preponderance" vrill be
active in the given direction ; and, in either case, its retard-
ing action is always due to the difference of the ascent and
descent. Therefore, in a series of inclines, some rising
and some falling, the effect in any given direction will
be proportional to the difference of the sum of all the
ascents and the sum of all the descents in that direction ;
therefore if it were required to know the preponderance of
the series of gradients given in the preceding form, it
win be necessary to multiply the corresponding tabular
number found in the fourth column by the length, and
setting the ascents in one result, and the descents in
another, and dividing their difference by the total length,
the result will give the preponderance in pounds per ton
in favour of that series of gradients irhose sam is greatest.
The following form is adapted for the purpose : —
Describe
Grarity ot
Product
Product
Indiiutlon.
whether
Lo«h.
of
of
lieeorfBU.
chaiu.
in lbs.
rijoo.
fBlis.
1 in 160
lise
«
14.00
560.
252
faU
32
8.89
284.48
490
faU
70
4.67
319.90
Level
level
45
132
rise
62
16.97
1052.14
-l&l
rise
18
483
86.94
920
m
91
2.43
221.13
100
M
28
22.40
62.72
261
rise
46
8.48
390.08
— -
2089.16 888.33
Divide by the Length
4p32) 1200.93
Preponderance due to the rises in poimd8=2.78.
The same result may he obtained in a less complex
manner, hut the shove form ^ves the ratios each separate
length of gradient hear, when compared with the whole
length; for instance, -7^ = 1.396 is the preponder-
ance in ponnds per ton due to the rise of 1 in 160; that is, if
1 in 160 were the only gradient, uid the rest of the hue
were a level, then 1.396Ibs. per ton repr
of power required over the whole line,
length of the gradient only ^ 40 chi
gravitation is 14db3. per ton; and the 1
individual preponderances due to the risei
those due to the falls, will give a total of
required in the given direction to overci
innue'tace of gravitation. When the trai
250
the same series of gradients, the preponderance is in
favour of the motion — ^that is, assists it ; because the rises
become falls and the falls rises. Hence the excess of
power required in the one direction, compared with that re-
quired in t/ie other, will be 2.78 x 2 = 5.561bs. per ton.
In order to compute the total excess at once without refer-
ence to the intermediate gradients, it is sufficient to know
the eflEective rise between one terminus and the other, and
the total length. Let H be the effective rise in feet, and
let L be the total length in chains ; then the rule for the
excess is -— -j; — ; and taking, for example, the preceding
data, we have H = 35.39 and L = 432. The excess in
this case, therefore, is —^ — -^ — '- — = 5.551bs. per ton,
the same as above. If the length is given in milesy the
rule for the excess becomes —^ — , and the above example
will work out - — -^ — '— = 5.551bs. per ton.
For the convenience of those who prefer a literal, instead
of an algebraical rule, I subjoin the following : —
Rule, to find the excess of power required per ton in one
direetion, compared with that required in the other —
Ist. When the " effective rise'^ in feet, and the " total
length'^ in chains are given —
Multiply the rise by 67.86, and divide the product by
the length: the quotient is the required ^^excess^^ in pounds
per ton.
2nd. When the ^^ effective rise^' in feet, and the " total
lengtV^ in miles are given —
Multiply the rule by 0.848, and divide the product by
the length : the quotient is the required ^' excess^^ in
pounds per ton.
ESSAY
ON THE POWER REQUIRED TO OVERCOME
THE RESISTANCE ON INCLINED PLANES.
As the Table of Gradients above described is not saffi>
cient to enable an estimate to be formed of the total
power required to put in motion a given weight of train
with a given- velocity, it is to approximate this object that
the following few pages are devoted.
The ordinary resistance to which a train is subjected
during motion may be separated into three kinds :
Istly. The resistance due to the frictiou of the carriages
and of their load.
2ndly. The resistance due to the air acting on the
surfaces of the carriages.
Srdly. The resistance due to the gradient.
I.— Of the Friction.
Eiperience has determined that, for all carriages con-
structed on the same principle and with the same dimen-
sions of hearings, gauge of rails, and general construction
of parts, the firiction is a conatant quantity for all veloci-
ties, and is expressed by a certain proportion of the weight
drawn. Therefore, if the symbol / denote this ennHtniit
proportion, and W the weight drawn,
pressing the total friction of the train.
If one carriage with its load weighs 6 tc
10 carriages, and if the proportion whic
tained by experiment is taken at 711
(/=7) X (W=6k10) = 420 lbs., which ii
- ance due to friction. But> in estimati
252
be overcomej besides the carriages^ the engine in fronts
being of a different construction^ should be taken into
consideration. Some experiments have shewn that the
friction of an 11-inch cylinder engine whose weight is
about 8 tons^ when running on 4 wheels^ is about 13 lbs.
per ton ; and a 14-inch cyUnder engine on 6 wheels^ the
weight being about 11 tons^ offers a resistance by friction
of 16 lbs. per ton. Supposing that an engine of the first
description were used, it would be proper to add to the
preceding calculation 8x13=104 lbs., making a total of
420 + 104 = 524 lbs. ; and if a 6-wheel engine were used,
as above described, 11 xl6=176 lbs. must be added, making
a total of 420+176=596 lbs. : the engine tender is here
supposed to be one of the carriages. But the above
allowance for engines must necessarily vary with their
construction and weight.
In general, for approximation, 4 carriages maybe added
for a 4-wheeled engine and tender, and 6 carriages for a
6-wheeled en^e and tender, and the gross weight of each
carriage (of the passenger class) may be taken at 5 tons ;
but this approximation must be understood to refer only to
a railway laid down with a 4 feet 8 J inches, or 5 feet gauge.
Hence, if n expresses the number of carriages actually
containing passengers or goods, the total resisting load for
a 4-wheeled engine is 5 (n + 4) tons, and the friction will
te (/= 7) X (W = 5 » + 20) in pounds.
II. — Of the Resistance of the Air.
The resistance due to the medium through which the
train pusses is divided into two parts — one being that due
to the direct or perpendicular surfaee exposed to th^
mediupi in the direction of the motioa^ ; and the other is
due to the lateral action of the particle? of air on the sides,
top, and liottom of the carriages.
First — To treat of the direct surface.
This is measured by the actual transverse area of the
railway carriages, with their wheels, springs, and frame-
253
work, such as would be represented on a geometric plane,
wliich is commonly called hj draughtsmen a " transverse
elevation" of the object. This area, then, is part of the
direct surface exp(»ed. Another portion is computed bv
supposing that the extreme mobility of the air enables it
to intersect and oppose itself to all the various openings,
comers, and parte not represented by the "trausvcrse
elevation," but which by their situation would be so if a
section were mad^ so as to expose them in front ; instead
of which, the air has access to them by tortuous and
indirect channels. With these parts must be included
the front surface of every succeeding carriage to the first,
as there is a large space between two carriages which very
freely permits the air to act on each carriage in succession.
From the immeuse variety of the dimensions and position
of the parts, it is quite impossible to arrive at any thing
more than an approximate measure of the surface ; but if
this be chosen with discretion, the error will not materially
affect the accuracy of the estimate.
Having ascertained the sur&ce, the nature of the resist-
ance is next to be considered. The motion of trains
through the air is so very variously influenced by the state
of the medium, in regard to its barometric and tbermo-
metric condition, and also in regard to the direction and
force of the wind at the time, which again is varied by
the winding course of the railway, that it is also on this
account impracticable to give a true solution to this prob-
lem. Therefore, in order to fix a standard to which these
calculations shall refer, let it he assumed that the air has
a constant barometric pressure of 30 inches, or 14.706 lbs.
per square inch nearly. The temperature is to be 60<»
Fahrenheit, and the air to be quite calm or at rest. Then
the resistance of the air will be measured by
force which the air itself would exert agains
surface if moving against it with the given velocit
over, since both theory and practice have establ
the resistance of air in motion varies as the
254
the velocity directly^ we derive the resistance offered to the
carriages when we know the resistance dne to some given
velocity. Thus^ if F is a given velocity^ and A is the
resistance due to it for a square foot of surface^ and V is
AV*
any other velocity, then, asFa:A::V: ^=aV* =
the resistance for any velocity when a = p •
With regard to the total surface of the train in direct
opposition to the air; let S represent the transverse
area, and include in this some allowance for the surfaces
of various parts indirectly exposed to the air. Also let Z
represent the firont surface of each succeeding carriage
beisides the first. This expression Z will be less than the
transverse area (S) by a quantity due to the obliquity of
direction of the impinging particles on the plane of the
carriage. This obliquity will depend on the variation of
distance between the carnages, and of their breadth
according to their construction. The following investi-
gation is suggested as a means of arriving at some definite
proportion of the whole to the effective surface.
In Fig, 1, let ABCD be the surface of the back.
Rg. 1.
and let there be another in
front of it of equal transverse;
and also let AE be the distance
between them.
By first considering the ac»
tion upon a simple plane only
in the direction of the motion.
In Fig. 3, the line AB shews the extreme limit of the
action of the uninterrupted
column of air rushing in from
the opening AC ; and the line
A C shews the other lunit for
the same opening : also each of
these lines may respectively
t^present the full force of the
255
air. Any intennediate line (AD) representa the force of
the air from one aide at the point J). In like manner
EC ED EB represent the force of the air upon the points
C, D, B, trom the other side EB ; tiierefore, the full action
on any point (D) is the joint action of the forces AD ED,
and by completing the parallelogram AFED the line
FD represents the force acting on the point D. But
because AFED is a parallelogram, AE ia bisected in G
by the diagonal FD, therefore the force on D is twice GD,
and also GC, GB, represent half the forces on C and B, and
generally the whole effect of the air on the surface CB
will be twice the sum of all the forces GD. Hence, in
Mg. 1, iff is a centre point in the body of a carriage
adjoining^e surface ABCD, the bundle of forces directed
against ABCD will be contained in the pyramid FABGD,
whose vertical axis is S AE.
InFigS, letiAD=AC = A, letEC = «,widBC=£,
FiR. 3. the force EB is /= Va* + «>.
- . A J But by reducing any force (EB)
f g ^ to its respective horizontal and
I e l— -'-'^ g 1 vertical forces, the intensity of
this force is diminished in the
ratio of the 4th power of the
cosine of the impinging an gle; the refore, at any point (B),
the radius being EB = Va= + «", and the cosine EC = a,
u;
the force -/a" + a^ becomes IT^^^'
The mean radius is EB = "-^^■^^+? nearly, therefore
the effective mean force becomes for the whole surface
,-,f^|^»d by putting J-.,
the whole effect will be for each foot of s
266
The rule I have adopted in computing the effective surfiEU^
^^ fmr~~7=^n when n is equal to the full breadth divided
(1 + 2 vi+n*) • ^
by twice the intermediate space ; and computiBg the pro-
portions due to the above rule^ we have —
When n =
€t
tt
€C
€i
1 the effective surface is ^
7
8
8
4
5
8
1
2
€€
€t
a
t(
6
ao-*
of the whole.
it
u
cc
tt
Assuming the third proportion to be nearest to the
practice in construction, and adopting this figure in the
estimate, the expression Z becomes S x ^, and for all the
carriages less the first *^*"" ^ expresses their resisting
surfiace; and adding the engine and tender, whichalso receive
a share of the direct action of the air, the total resistance is
found in the formula — ^ — - x a V*.
It now remains to give some expression for the lateral
resistance of the air. Let K represent the actual measure-
ment of a railway carriage, such as would be represented on
a drawing denominated a '^longitudinal elevation^^ of the
object, and to this surface add some allowance for those parts
which are likewise indirectly exposed to lateral action.
For all trains in motion there must necessarily be a current
of air directed against the sides of the carriages, caused
by the eddying motion given to the air displaced in front
by the forward motion, which then acts along the sides of
the carriages in its endeavours to reinstate itself. This
action of the air cannot be accurately appreciated ; yet
some accoimt should be taken of it, as, however trifling it
may appear, the surface exposed to it is very great, varying.
257
in truss of 10 or 15 carriages, from 5,000 to 10,000 aqnare
feet. Then let / represent tbe resistance due to one
square foot. / E (n + 2) is the whole lateral resistance ;
and the whtAB resistance lateral and direct is ex-
pressed hy riiilJL« + K/(n+2)] x V, and making
Q = ' '" 3 ^^ " + K / (» + 2) it hecomes QV.
It will he proper now to give some value to the coefS-
cients a and /. The first is foiind hy the well known laws
of pneumatics. The height of the nniform atmosphere
which surrounds the earth is computed to be, on an avenige,
26,400 feet. Eight times the square root of this hei^t
will give the velocity with which the air will rugh into a
vacuum, therefore 8 -/26400 = 1300 feet per second.
Tliis velocity is due to a pressure of 14.71 lbs. per square
inch, or 2118 Ihs. per square foot of surface. Hence the
pressure on a square foot with any other velocity m^ be
found, because the pressures vary as the squares of the
velocities. ^ " — = velocity of airin vacuo in miles per
hour. Now as ^^°^,' ^^' : 3118 :: V: ^=re8i8tance
22" 370
due to any velocity V. Hence a = — -
By some observations I made in a train moving at the
rate of 80 miles per hour, the air being quite calm at the
time, I found that the cnrrent against the carriages was
acting at an angle of 9 or 9 J degrees nearly, and computing
the force (which varies as the square of the sine of the
uigle) we have this proportion —
> V 1 (sine "Q ) V
Moreover, this quantity / will vary with tl
the disturbing force producing the current
velocity, and therefore the angle varies. 1
258
the cause which produces this angle varies as the square
of the velocity, we have this proportion to find the
true value of /. Since the angle given is known to
be due to thirty miles per hour vdodty, then as
80« = 900: -i~ :: V : -— ^ — = Z. The lateral
14400 12,960,000
current of air does not act on the entire lateral surface of
the train, because the air, after acting on the front surfaces
of the carriages, is repelled therefrom, and, escaping
laterally, passes along the carriages in continuous eddies,
thereby neutralising part of the effect of the currents
directed against them. No accurate measure can be given
of the effect produced ; it depends partly on the proportion
between the lengths of the carriages and the intermediate
spaces. If we assume that the current begins to act upon
the carriages after the train has traversed a space equal to
twice the intermediate distance, and if the length of the
carriages are taken at a medium to be three times this
distance, then the side surface effectively exposed to the
lateral current will not be more than one-third of the
whole. I therefore, in default of better data, assume this
proportion; and, by substituting thesevaluesof a and /, in the
equation of Q,we have Q=tS!tl^ x -L + E!tl2l x — -^—
^ ' 2 370 3 12,960,000.
For convenience of calculation, the values of S, K, »,
should be determined, so that every thing relating to an
estimate of power may refer to a standard. According to
the existing practice in the construction of carriages, I
estimate the value of S to be 80 square feet, including the
allowances for indirect action. The value of K also I take
at 600 square feet, with similar allowances. With regard
to n, I assume as a standard 100 tons weight drawn,
including engine and tender ; and supposing these last
together weigh 20 tons, the remaining 80 tons divided by
five (the average tonnage per carriage) will give 16 car-
riages, or 131 = 16^
259
Substitating these values in tlie equation of Q, we have
Q _ 8006 + 3) ^6ooMi6+2)V!^ 2 054 ^ JV1_ Hencethe
2 x 370 38,880,000 3600
second item of the resistance to motion is
To fadlitate the application of the preceding rules to
practical cases^ I subjoin a table which will embrace all the
different values of S, K, and V, and the variable propor-
tion (indicated by the symbol w) of distance between the
back carriages. The general rule for the resistance of
theairis QV3= S^l [(^ + 1) a?+ 1] + KV^ (» + 2)
370 ^ 38,880,000
in pounds avoirdupois.
261
To estimate the resistance of the air by the tables^ when
the nnmber of carriages (n) is given^ exclnsiye of engine
and tender, let the formula become QV* = SN + K (» + 2),
Look in table S for the number corresponding to the
given velocity and &ont surface, and in table N for the
number corresponding to the number of carriages (n), and
to the given proportion of the intermediate space to the
breadth of the carriage {a:), and multiply the tabular num-
bers found together; and to this product add the product
ofn + 2, and of the tabular number in Table K correspond-
ing to the given velocity, and the side surface of each car-
riage. This sum will give the resistance required. To
illustrate this by an example —
Let t? = 24 miles per hour.
f< s = 70 feet front surface.
" » = 12 carriages*
" * = 600 feet side surface.
'^ a? = half the breadth = intermediate space.
In Table S,
Opposite 24, and under 70, we find - - 108.97
In Table N,
Opposite J, and under 12, we find - - 5.5
The product of these^numbers is - - 599.33
In Table K,
Opposite 24 and under 600, we find - - 5.12
and 71+2 = 12 + 2= - - - - 14
The product ofthesenmnbers is - 71.68
And ttie sum of 599,33 + 71.68 = - - 671.01
is the resistance sought in pounds.
III. — Of the Gradient*
The force exerted by a body osk BXk inclined plane is to
the weight of the body as the height c^ the plane is to its
length ; and this force tends to cause the body to descend
the plane. Sut if the motion of the train is up the incline,
262
then the force acts in resistance to this motion; andif the
motion is down the incline^ then it acts as an assistant to
the propelling force applied to overcome friction and
atmospheric resistance. Therefore^ this term of the equa-
tion of total resistance is expressed + -- or — ii. when
,9 9
g is the ratio of the length of the inclme to its height,
the term + being used on ascending, and the term — on
descending inclines.
Summary of the Resistance.
From the foregoing investigation, it appears that
the total resistance to be overcome, to move 100 tons
along with some velocity (V), along any gradient
{g) is expressed by the formula, in pounds = 700 +
2.054 V« + ^ ± 2il!229. And the general rule is
(5 n . 20)/. *i2-^ r^^^Ll^^ pounds.
^ ^"^ 740 38,880,000 g ^
Also, the equivalent for n in the terms of W, may
be inserted. Let g express the number found in
the 4th column of the table of gradients, instead of
^^% and inserting the previous values of (s) and (K),
i/becomes Wf 1 Wff . (^T^' . (^-12)1!, or
46.25 324,000 '
W(/- ff -^ 46.25 "*" 324,000/ gjs — 32^400^ ^^^difthe
velocity were assumed to be at an average of 30 miles
per hour, and the friction at 71bs. per ton,* the rule
becomes W (29 ±g)— 122. If the weight were 100 tons,
the resistance in pounds becomes 2900 + lOOg. Therefore,
the number 2900 expresses the resistance in pounds of 100
tons moving along a level plane at the velocity of 30 miles
per hour, which gives 29 lbs. per ton, or is equivalent to the
gravity of an incline of one in 77 J. Any incline, therefore,
whose descent is not in a less ratio than this, will not cause
the train to accelerate its velocity (being already 30 miles
per hour) by gravitation.
263
SelatioH of the Power required to the Retistanee.
I will conclude this essay by shewing briefly the relstioo
existing between the resistance of the load and the power
of the engines required to draw it along. I resume the
data upon which the resistance was formerly computed,
and which are recapitulated as follows : —
Friction of each carriage, Tibs, per ton.
Carriages weigh each, 5 tons.
Engine and tender computed as 4 carrit^es.
Weight drawn (including engine and tender weighing
20 tons) 100 tons.
Front snrface of each carriage (with allowance for
concealed surface) 80 square feet.
Side surface of each carriage (with allowance for
concealed surfaces), 600 square feet.
Space between carriages, three-quarters the breadth
of a carriage.
Velocity of motion, 80 miles per hour.
The rule for resistance due to the above data is
3900 ±100 if in lbs.
To draw a train along a railway, the power of traction
depends upon the adhesion of the drivmg wheels to the
rails. This adhesion, therefore, independently of the in-
clines, must equal SQOOlbs.
But in estimating the power, it is necessary to take the
most extreme cases which may occur on the railway, that
the engine may surmount with its load the steepest inclines.
In the more recent practice of engineers, the inchnation
1 in 200 is not un&equently adopted as the standard
gradient, and to this I will confine myself, as, when inchnes
are much steeper, the speed is practically considerably
reduced below 30 miles per hour. On referrin ' "
table of gradients, opposite 1 in 200, column 4th
11.20 lbs. per ton, which gives 11.3 x 100 = ]
for the resistance due to the gradient. 1
adding together 3900 + 1120 = 4020 lbs.
required to enable the engine to draw the loa
364
given speed. The adhesion varies very much, owing
partly to the liability of the wheels to slip or skid on
greasy rails, partly to casual imperfections in the rails
or machinery, and partlv to inappreciable obstructions,
oscillations, and irregulanties of motion. It will also vary
owing to the different manner in which the weight of the
engine is supported on the wheels, either by the driving
wheels being coupled or imcoupled, or by there being six
wheels to carry the weight; also, the diameters of the
wheels being Afferent cause great variation in the adhe-
sion; and ako, by varying the construction of the engine,
the weight imposed on the driving wheels may vary fix)m
|- to I ofthewhole. 'A combination of the above causes
produces great uncertainty, to avoid which Ihave fixed as a
standard, that the adhesion, under the least favourable cir-
cumstances, of an engine weighing 12 tons, whose weight on
the driving wheels is 8 tons (being two-thirds of the whole)
is one-sixteenth part of the weight of the engine when the
driving wheel is 5 feet 6 inches in diameter, and this pro*
portion will vary inversely as the diameter of the wheel.
Supposing that such engines are used, then the adhesion
of one engine is P ^ J^^^Q = 1680 lbs.; and in order to
enable a train opposing a resistance of 4020 lbs. to be
moved at 80 miles per hour along an incline of 1 in 200,
three engines would be required at least.
Pursuing the investigation to ascertain the commaxial
expenditure resulting from the use of the engines to draw
the load as before given, I have considered that the best
measure of the effect would be the cubic feet of water
vaporized under a given pressure in an hour, in preference
to computing the horses-power, or the lbs. raised 1 foot
high. By knowing the performance of the boiler as to
the supply of steam, we can find the real effect produced
by an engine, when the resistance due to the given unilbrm
maanmum velocity is determined.
265
The quantity of fuel which will cause the vaporization
of a cubic foot of water, multiplied by the total vaporization
will give the required commercial eflEect. I will suppose the
case of an engine with a 12-inch diameter of cylinder
(whose area is a inches) ; stroke of the piston 1 foot 6 inches
(the length being / in feet) ; the driving wheel being
5 feet 6 inches (indicated by the symbol D in feet) ; the
speed as before being 30 miles per hour (or V miles).
Then the general expression for the quantity of steam used
by the two cylinders in one hour, allowing for the waste
, ., o 4.4/0. 5280 x7V 51.33 /«V
in the passages, &c., t±i5 x WB^ ^ "HD —
The relative volume of steam at 60 lbs. per square inch,
compared "vrith the water generating it, is 880 : 1 ; there-
fore yg X ^ = .135 ?^ = cubic feet of water vapo-
rized per hour. Then substituting the values of laY and
D, we have 124.8 cubic feet of water required per hour for
one engine, supposing it was fully employed. The actual
power transferred from the cylinder to the circumference
of the wheel at the point of contact with the rail is measured
by the pressure on the piston, reduced in the ratio of the
length of the stroke to the diameter of the wheel.
Let (/?) represent the pressure (60 lbs. on the inch), and
let the previous notation be used, then the general expres-
sion of the power is yr- for one cylinder only. The ratio
between the greatest effect of one crank, and the mean
effect of two acting simultaneously at right angles to each
other, is nearly as 10 to 16 ; and adopting this proportion,
we have 1.6 t^ ^ ^ power of two cylinders. Hence,
substituting the values oi pal and D, we have 2960 lbs.
nearly for the power of one engine ; and the power of the
three engines necessary for adhesion will be 2960 x 3 =
8880 lbs., being 4860 lbs. in excess of the resistance. This
F F
266
excess will be partly taken away by the additional friction
of two extra engines and tenders^ and the corresponding
indirect front and lateral atmospheric resistance^ and the
gravity of 40 tons extra on an mcline of 1 in 200. This
extra resistance will not exceed 800 lbs., and the whole
resistance will be 4020 + 800 = 4820 lbs ; therefore, the
power which can be obtained is more than that which
is reqnired in the proportion of 8880 : 4820 : : 1.84 : 1.
To reduce this supply to the demand, we may reduce
the Tai^ri^tion of 124.8 cubic feet in each boiler by 1.84,
and then we have ^^'\/ ^ ^ 203^ cubic feet to be actu-
ally converted into high pressure steam.
The above computation refers only to the ca«e of an
ascending gradient; but, of course, it is proper to estimate
the case of a descending gradient, to obtain a true mean
value of the effect. Therefore, supposing that the same
weight is returned along the railway, we have 2900 —
1120 = 1780 lbs, for the resistance. One engine alone is
nearly equal to the duty as regards adhesion, which is 1680
lbs. ; but it is better to use two to be certain of the duty re-
quired, owing to the variation to which the adhesion is liable.
The power of one engine being 296jO lbs., two engines would
exert 5920 lbs., from which suppose 400 lbs. to be deducted
for the resistance to the extra engine, 5520 is the effective
power which can be exerted, bearing a proportion to the
resistance of 3 to 1 nearly. Hence, if the steam is gene-
rated at the full pressure of 60 lbs., and is allowed to
expand to 19.3 lbs. pressure in the cylinders, only —
o. 1
of the full complement of water is necessary; that is,
instead of requiring 124.8 x 2 = 249.6 cubic feet,
^^^ = 80.5 cubic feet are sufficient. Therefore, to go and
return a journey of 30 miles in one hour, 203.4 + 80.5 =
283,9 cubic feet of water are required ; and reducing
267
this quantity to simple tenus^ we have an average of
— '— = 9.46 cubic feet of water required per mile for 100
tons load, when travelling 30 miles per hour, on gradients
whose constant ascent and descent are 1 in 200. This
estimate is not exactly applicable to a level line, though
the aggregate resistance in both cases is nearly the same,
the ^fference in favour of the level being due to the
resistance of the extra engine. For on the inclined railway
we have the resistance 4020 + 800 + 1780 + 400 = 7000;
on the level we have the resistance 2900 + 400 + 2900 + 400
= 6600, being 400 in favour of the level, equal to the
resistance of one extra engine. On a level, the resistance
being 2900, two engines are necessary ; and the effective
power being 5520, the proportion of power to the resist-
ance is 1.9 to 1 nearly. Hence, the steam can be allowed
to expand from 60 lbs. to 31.6 lbs. in the cylinda*, and
quantity of water required to be vaporized is ^^^'^ ^ . ^ =
262.8 cubic feet, that is 8.76 cubic feet per mile, shewing
.7 of a cubic foot in favour of the level. '
It now only remains to shew what duty one engine may
be put to ; the gradient, velocity, and other proportions
being the same as before.
As the adhesion is the limit of the power, and conse-
quently is the measure of the resistance the engine is
capable of, it follows that 1680 lbs. is all that is required
to be exerted by the cylinders. Hence, the resistance
will bear a proportion to the whole power the engine can
exert (= 2960 lbs.) of 1 : 1.76 nearly; therefore, expanding
the steam from 60 to 84 lbs. in the cylinders, the vaporiza-
tion of ?^^ = 70.9 cubic feet of water is the limit of effect
1.76
required. Also we have this equation of the power
required given in terms of the number of carriages drawn
(/ = 7) X (5« + 20) H- ('■—= 194.59) x Q~±^)
F F 2
268
(
KV«
38,880,000
= 12.5) X (« + 2) + (^ = 11.2) y (5» + 20)
- 1680, and reducing this equation n = '-^^^' •
This will give 16 carriages^ equal to 16 x 5 + 20 = 100
tons descending, and 5 carriages, equal to 5 x 5 + 20 = 45
tons ascending ; also, we deduce that the engine can draw
eight carriages =8x5 + 20 = 60 tons on a level.
For the convenience of those who wish to calculate the
vaporization required with pressures in the boiler different
from the assumed standard of 60 lbs., I subjoin the
following table of relative volumes of the steam compared
with the water generating it : —
Presmre per
BelatiTe Volnine
iquareinch
of Steam,
above
that of water
atmoflphere.
being 1.
70
340
65
359
60
381
55
406
50
434
45
467
40
506
35
552
Water vaporized
per hoar at maximum,
power of Engine.
cubic feet.
139.6
132.2
124.5
116.9
109.3
101.6
93.8
86.0
Maximum power
of one engine, at the
point of contact
with the rail.
lbs.
3453
3206
2960
2713
2466
2220
1973
1727
Prom the above table it is easy to determine any modi-
fication of the preceding calculations the reader may think
fit to make.
It is necessary to state here, in concluding this portion
of the essay, that so much does the capability of an engine
to draw a load depend upon the state of the rails, that the
preceding estimate of adhesion = 1680 lbs. may be con-
sidered as very low ; indeed, experiments and observations
have been made, showiiig that the adhesion varies £rom
-th to ^th of the weight on the driving wheels ; this
269
great variation being consequent upon the temporary
circumstances of weather, cleanliness, and state of repair
of the metals ; so that, since the preceding calculatioi^s are
founded upon the lowest datum, the capability of an engine
may possibly be increased two or three times that which is
indicated by the results I have given. It appears that the
cylinders are capable of exerting a power equal to 2960 lbs.
with steam of 60 lbs. pressure ; therefore, in ordinary cir-
cumstances, the adhesion may be estimated as equal to this
power. This will give an increase of effect produced much
above the calculated effect ; for, by estimating the term
1223.12, in the equation of n, to be increased by adding
to it (2960—1680 =) 1280, and therefore making this
term = 2503.12, we shall find that
A descending train may be = 150 tons.
An ascending train may be = 85 tons.
A train on a level may be = 105 tons.
The boiler, in this case, must vaporize its maximum
quantity of steam. It is also obvious that, under very
favourable circumstances, the adhesion maybe much greater
than even this estimate; so that by increasing the pressure
of the steam a greater velocity can be obtained, or by
enlarging the diameter and stroke of the cylinders much
greater loads may be drawn. Further, if instead of em-
ploying one pair of driving wheels, the two pair of a four-
wheeled engine are coupled, then the whole of the etigine
is exerting its weight to produce adhesion. In the case
which I have assumed, the engine weighs 12 tons, with
8 tons resting on one pair of wheels ; but if the machinery
is so constructed that 6 tons may rest on each pair of
wheels, then the adhesion will be increased one-half more ;
or the tractive force, instead of 2960 lbs., may be estimated
at 2960 + 1480 = 4440 lbs. Therefore, the term 2503.12,
in the equation of n as last determined, may be increased
by 1480, which makes it = 3983.12. Hence we shall
find, that, in ordinary cases, a four-wheeled coupled engine
is capable of drawing
270
A descending train = 230 tons.
Or an ascending train = 125 tons.
Or a train along a level = 155 tons.
The reader is requested to bear in mind, that the num-
bers here given are only comparative, and that they depend
entirely upon the data assumed in the foregoing pages.
In consequence of the many varying circumstances of con-
struction and other conditions, I am compelled to give a
general illustration only. It is not withm the scope of
this essay to enter into further particulars, which more
properly belong to a treatise on locomotive engines ; and
therefore, such readers as desire to obtain a knowledge of
the details which govern the mechanical action of an engine,
will find the subject amply discussed in works ably written
by the Comte de Pambour, Mr. Wood, and others.
ACCIDENTAL CAUSES OF RESISTANCE.
The resistance of a train as brought forward in detail in
the course of this essav is all that can be taken into account
when forming a general estimate ; but there remain two
important accidental causes of resistance, which it is not
improper now to mention. The first cause which I shall
draw attention to is the resistance opposed by the wind.
The second cause is the resistance opposed by the journey
of a train along curves on the Kne.
The Resistdnce of the Wind.
I have hitherto considered that the air through which
the train passes is quite calm, or at rest. But this is very
seldom the case; and though, when gentle winds are
blowing, the effect on the surface of the train is not very
remarkable, yet strong winds will produce a sensible retarda-
tion of velocity; or an additiontd tractive force is neces-
sary to overcome the resistance of the wind, and maintain
the required velocity nnimpaired. As the wind may arise
from any point of the compass, but the direction of the
railway is fixed, the wind will impinge, generally, in an
271
obKque direction upon the surface of the train. It is,
therefore, necessary to determine such a general rule as
shall meet any given circumstances of direction.
Suppose that the wind acts upon the train at some given
angle contained between the directions of the wind and
train respectively. The force which the wind will exert in
its true direction is ^, when Y is the wind's velocity in
miles per hour. This diagonal force can be resolved into
two forces; one acting perpendicularly and the other
parallel to the direction of the train. That which is per-
pendicular is proportional to the square of the sine of the
given angle, and the force is represented by the expression
sine* X —-. This force, whichever waythe train is moving,
is constantly soliciting it to act against the side of the
opposite rail, and tends to produce friction. The force
which acts parallel with the train^s direction is proportional
to the square of the cosine of the given angle, and is repre-
sented by the expression cos.2 x Jl . This force, accord-
ing as its resolved direction and velocity is opposed to, or
composed with, the direction and velocity (rf the train^
requires an increase of the tractive force, or becomes itself
a propeller. The symbol Y expresses the absolute velocity
of the wind ; but since trains in motion are now under
discussion, the expression above given will indicate only
the effect produced on a train at rest. The real effect
of the wind is due to its relative velocity. If the wind
and train are moving in the same direction, the wind can
produce no effect unless Y = V = velocity of the train*
Therefore, in this case, V — Y = Z is the effective velocity
which aids in propelling the train when V is less than Y ;
and V + Y = Z is the effective velocity which opposes
the train when the wind and train move in opposite direc-
tions. Also, when V is greater than Y, and the wind
moves with the train, the effective velocity is V — Y = Z^
which wiU oppose the train. But in the fbrmer part
an
of this essay we have already estimated tlie effect due
to V^ (corresponding with the velocity of the train) ;
therefore, the expression which will correspond with the
velocity of the wind only, is Y' ± 2 VY = 7?. The sign —
being used when the wind and train move together, and
the sign + when in contrary directions; in both cases
acting in opposition to the train^s motion. Also, the
sign — , is used when the wind and train move together;
and the term Y being greater than Y, the wind assists in
propelling the train. Therefore, the general expression,
cos.» X i-. will now become cos.^ x - = cos.' — .
371 371 371
All winds may be considered as blowing in a horizontal
direction ; therefore in estimating the amount of surface
..^ .. the W exp^ssed b, .ine- ^^. i. U .ot
necessary to estimate the tops, bottoms, and the reverse
sides of the carriages ; and the opposed surface will be
sufficiently taken, if the expression K, which represents
the side surface, be made — : then the resistance due to
the wind acting on the sides of the carriages of thewhole train
will be indicated by the expression sine^ x M5_2) ^ Y ^
The surface exposed to the force expressed by cos.^ x -_
varies according to the angle of direction of the wind, and
to the intermediate distances between the carriages. When
the angle does not exceed a certain number of degrees,
the whole front surface of the carriage is not exposed to its
action, part of it being sheltered by the adjoining carriage.
On calculating these limits due to the different intermediate
spaces, I find that when the intermediate distance
Is equal to the breadth.
00
45 deg. min.
Is 7-eighths do.
48 « 48 «
Is 3-fourths do.
53 " 7 "
Is 5-eighths do.
a;
57 " 59 "
Is 1-half do.
^
63 " 26 "
273
fience, an; angle wliicli is less than tlie angle due to tlie
given intermediate distance will not permit the whole front
Bur&ce to be acted upon by the wind. If the front surface
be espresaed by S as used in a former part of this essay,
and X express the fraction of the intermediate space when
the breadth of a carriage is — I, the actual surface exposed
will be SX X — ', and the resistance mil be expressed by
^^ — ^^, and for the whole train it becomes
SZ' (3^ + it^) ^^'-"""- ). To facilitate the compu-
tation of these two forces I subjoin a table. The first
column shews the impinging angle for every five degrees
of the qiutdraut. The second column gives a divisor
(L) due to the coefficient of the perpendicular force
= sin.* Jt - ^ .-■ The remaining columns give the divisors
(F) due to the coefHcient of the parallel force= X (con. " «n.)^
274
L
DiTtoor dii*
to literal
F DIVISORS DUE TO THE FRONT SDBFACB.
Degree of
angle of
later. tpM*.
hiUt.tftet.
Inter, tpaoe.
r.ler. iptct
Inter, ipace.
Incidence.
wirfiK«.
= 1
"i
= *
= »
= i
iuf.
inf.
inf.
inf.
inf.
inf.
5
195348
4273
4883
5697
6837
8546
10
49212
2169
2479
2892
3470
4338
15
22152
1484
1696
1978
2373
2968
20
12684
1154
1319
1538
1846
2308
25
830a
968
1106
1291
1549
1936
30
5936
856
978
1141
1371
1714
85
4506
789
902
1052
1352
1690
40
3591
753
860
1004
1206
1506 ■
45
2968
742
848
989
1187
1484
50
2529
898
898
1004
1205
1506
55
2211
1127
1127
1127
1352
1610
60
1978
1484
1484
1484
1484
1714
65
1806
2077
2077
2077
2077
2077
70
1680
3171
3171
3171
3171
3171
75
1590
5538
5538
5538
5538
5538
80
1530
12303
12303
12303
12303
12303
85
1493
48837
48837
48837
48837
48837
90
1484
inf.
inf.
inf.
inf.
inf.
The use of this table is as follows :
To find the resistance against the sides of the train:
Multiply together the square of the wind^s velocity = Y',
and the total lateral surface = K {n + 2), and divide this
product by the number in column L due to the impinging
angle ; the quotient is the resistance in pounds.
To find the resistance against the front of the train:
Multiply together the square of the wind^s eflfective velocity
__ Y^ + 2VY, and the front surface = S ; also divide the
number of carriages plus one by the number in column F,
corresponding to the impinging angle and the interme-
diate space^ and to the quotient add .002692; then multiply
the first product and this sum together : the result is the
resistance in pounds^ which becomes positive or negative
275
dependent on the direction and the velocity of the train
as already pointed out.
The Resistance of Curves.
As lon^ as the train proceeds over those portions of a
railway which are straight^ the progressive motion is not
disturbed by lateral forcible contact with the rails, because
there is no disturbing force which urges the wheels to leave
the rectilinear course in which they move in accordance to
the laws of dynamics. But when the train arrives at such
portions of a railway as are laid down in a curvilinear
direction, then the flanges of the wheels, by reason of the
dynamical law of progression, come into contact with the
rail whose radius is greatest, so that during the train's
progress along the curve they are constantly urged to
impinge on the rail, which diverts the wheels jfrom their
tendency to continue motion in a right line. This con-
tinual contact between the flange and the rail is a source
of resistance which I propose to investigate. It is well
known that when a body is made to revolve round a centre,
it is acted upon by two forces ; one urges the body forward
in the direction of the tangent to the circular path of the
body, and the other urges the body towards the centre of
revolution : the combined action of these two forces keep
the body in rotation. The latter force is equal and oppo-
site to another which urges the body to fly from the centre
and to seek a rectilineal path, and which is called the
centrifugal force of the body. This force may be easily
appreciated by observing the effect of a common sling which
a man puts into rs^id revolution. As long as the man holds
the strings together the sling revolves; but when he lets one
of them sKp, the stone Or weight in the sling is liberated and
goes forward in a straight Une. The force urging the body
towards the centre is measured by the tension on the string,
and this tension is equal and opposite to the centrifdgal
force. In like manner when a train moves along a curve
the tractive power would urge the carriages in a straight
line were they not confined by the rail> the pressure
276
against the rail is the measure and effect of the centrifugal
force, and the friction consequent on the pressure is the
measure of the resistance to progression. The rule given
in all works on mechanics for ascertaining the centrifugal
force is ~ =P when Vis the velocity in feet per second
32 >< R • . '
R is the radius in feet, W is the weight of the body.
But in this work we shall require that
V = velocity in miles per hour.
r = radius in miles.
W = weight of the train in tons = 5 (w + 4).
P = centrifugal force in pounds.
The above expression becomes P = — -^ = zUl^Lz),
Engineers have generally attempted to balance this cen-
trifugal force by making the exterior rail of the curve of
such an elevation above the interior one, so that the gravity
of the carriages will cause them to descend a transverse
inclined plane, whose length is to its height as the whole
weight of carriages is to such a portion of it as will balance
the centrifugal force. In order to estimate this inclined
plane, let ff be the gauge of the rails in feet ; and h the
elevation of the exterior above the interior rail, in inches.
Then as ^ : *- : : 5 (» + 4) x 2240 : ^^Ol±±).
^ 12 ^ 7r
■WTO
Hence A = J^ in inches.
6533 r
It is necessary to fix some velocity by which the value
of h may be determined, and, of course, the maximum
velofeity should be assumed, as then any less velocity cannot
produce sufficient centrifugal force to surmount the incUne.
It is, moreover, worthy of observation, that the elevation
of the exterior rail is idtogether independent of the weight
drawn. The following is a small table adapted to a velocity
of 30 miles per hour as a maximum, and a gauge of rails
= 5 feet. The elevations corresponding to any other gauge
miay be found by multiplying the tabular number by the
assiuned gauge, and dividing by five.
277
ItadiuB of
Height of exterior
Radius of
Height of exterior
curves.
rail above inte. rail.
curve.
rail above inte. rail.
in miles.
in inches.
in nules.
in inches.
*
2.7564
2
.3445
i
1.3782
2i
.2756
i
.9188
3
.2297
1
,6891
34
.1969
1}
.5513
4
.1722
.4593
5
.1378
U
.3938
6
.1148
It may^ therefore^ be assumed that the centrifugal force
is balanced by the elevation of the outward rail, and that
resistance will not ensue from this cause. The principal
remaining cause of resistance is the tendency of the wheels
to impinge against the rails, causing the carriages to oscil-
late from side to side. This takes place in the following
manner : — ^When the train leaves the straight line, and
comes into the curve, it continues its direct motion till the
wheels strike the rail very obliquely. The carriages then
recede from this raU at an angle of recoil equal to that of
the impingence, and continue motion in this oblique
direction till the other wheels strike the other rail, when
they again recede, and the same degree of oscillation is
continually repeated. This obliquity is measured by the
small angle contained between the rail and the wheel; and
the angle, when greatest, is due to the arc of a circle
whose chord is in the direction of the wheels, and which
contains, in a portion of its length, the distance between
the extreme points of intersection of the outer circum-
ferences of the two sets of carriage wheels, and the upper
surface of the rail, being also the extreme points of contact;
and, at the end of this distance, the versed sine is the
difference between the gauge of the rails and the gauge of
the flanges.
I have been particular in describing these measures,
because fipom them only we can obtain the measure of the
chord of impingence, as will presently be seen.
278
The diiFeveBiOe of the gauges varies fipom } of aa inch
to li inches with diffirarent engineers and builders. I
will assume a mean diiSerence of 1 inch^ which gives half
an inch on each side between the flange and the rail when
the train does not oscillate. It is needless to take any less
dimension for the versed sine, because, during the repeated
oscillations that ensue, the flange must be in contact with
the rail on one side of the line, leaving a space = 1 inch
between the flange and the rail on the other side. Also,
in consequence of these oscillations, one of the &ont wheels
will be in contact with the rail on one side, while the
opposite beck wheel is in contact with the other rail, and
so on ; therefore, the distance of the wheels measures a
proportion of the chord ooljy which dqpendB for its ratio
oa the radius of the curve.
It is required to find the length of the chord. Let
the distance of the wheels measure from the point of
contact = a, and the versed sine at this distance = b ;
let the length of the half chord = c, and the versed sine of
the half chord = a? : the radius of the curve, as before, = r.
Then, a, b, and r are given to find c and x. Since the arc
in this case is very inconsiderable when compared with the
whole circle, we will suppose that the versed sines vary
as the squares of the chords with which they are found.
Therefore c — a is the length of the half chord with
which the versed sine x -^ b is found. Now, as
(? : (c — a)« :: 07 \ x — i, or ^ = ^ « >. By the properties
of the circle x is also = r — ^/i^^f^ = -- very nearly ;
hence — ^^^^ = — , or %rb -=^ Zac — a 9 and
C = ^rb^a\ then if ^= in, C =?■. I, and ^ = {am^2r)\
But the sine of the angle which the wheel makes with the
rail is measured by Zx, or (^"^ + ^^) when the radius is c.
»79
AlsOf when the length of c is known^ the number of oscil-
latioDs due to the impingence on the cur?e in a second
ifill be k: Hi, when V ^ velocity in miles per hour.
xOC
Before we proceed to estimate the force which produces
resistance on the curve, it is necessary to explain another
cause of the oscillations not yet noticed.
All the engine and carriage wheels are made of a conical
form, tapering outwards, 'Ihe object of this form is pur-
posely to correct the tendency, we are now discussing, of
the wheels to strike the rails while going round a curve ;
for the instant the wheels move laterally on the rail^ those
on one side, in consequence of their tapering form, enlarge
their diameters } while those on the other side are equally
diminished ; therefore, the velocity of the wheels on the
outar rail of the curve is greater than that of the inner
ones ; and if the velocities of both are in proportion to the
inn^ and outer radii of the curve respectively^ it is evident
that there would be no tendency of the wheels to strike
the rails, but they would always continue motion in the
direction of the tangent to the curve. All that theory
requires is, that the carriage wheels should have such a
taper, that the increase of velocity in moving laterally
one indi shall be to the whole velocity as the gauge of
the rails is to the inner radius of the curve. If d repre-
sents the diameter of the wheel in inches, and / the taper
of the tire for an inch of the breadth thereof, it is evident
that d will be proportional to the whole velocity when
2t is the increase, therefore d : 2t :: r : a or t = ^. If
the diametCT of the wheel is 42 inches, the gauge of the
rails 5 feet, and the radius half a mile, we shall find
t = ^th of inch nearly, for each inch in breadth of the
tire. Bat> practically, this conical form does not generally
secure the object it is designed for. The taper having
been once determined upon, can never be varied as the
circumstances require; for, ctBteris paribus^ the taper
280
ought to vary inversely as the radius of the curve, which
it cannot, and hence arises that cause of oscillation which
I have alluded to : but, as regards the increase of resist-
ance fipom this cause, it will ultimately appear to be very
insignificant, and need only be considered in extreme cases.
I will suppose, for the sake of argument, that the taper
is calculated for the worst, that is, the sharpest curves of
the railway. When the wheels have enlarged their diame-
ters by the lateral motion, the increase of velocity is ex-
pressed by —". The mcrease of velocity proportional to
the radius of the curve should be = ^ : therefore, as the
r
taper which is proper for the worst curves will give too
great an accession of velocity to any other curve, we have
V (— — ^) for the relative velocity which will cause thewheels
d r
to rotate round a centre whose radius is S . But this rota-
tion produces a centrifugal force which impels the wheels
already oscillating into a still more rapid state of oscilla-
tion. The measure of this centrifugal force is expressed
by the equation = 1505.8 / V^ x ^— =^'. This force
in conjunction with that due to the angle of impingence,
increases the number of oscillations computed by the chord
c, in the proportion of the latter force to the sum of the
two : and the chord c will be shortened in the same ratio.
The force p, due to the angle of impingence, is to the
whole force which propels the weight of the carriage, as
the sine of the angle = (?!? + 2r)' to the radius = ?5L±_2r ;
and p = 5600 x «.5±2r. The sum of the two forces becomes
mr
= 5600 ["■^'^jiJr + ,2689 t V x ^'^*^~^^\ consequently
the number of oscillations will be
= V X 1^^^ H- .7887 V X ^ X (f- ^^', and
flwi + 2r or gr {am + 2r)'
281
when is known, the length of the chord of impiugence is
22V
I 15,0
I In order to enable the reader to apply* these rules prac"
ticaUy, I will assume such general dimensions as will sim-
plify the formula, and then give a practical example in
illustration.
Let the distance of the wheels, as specified in a former
page, be a = 8i feet, and the lateral play of the wheels be
d = 1 inch, then -? = w = 100. Let the diameter of the
o
carriage wheels be rf = 42 inches, and the taper of the
tire be /=.05 inches ; let the gauge of the rails be^=5 feet,
also let V = 30 miles per hour, and let r be given in miles ;
so in that r in the formula becomes 5280r. With these
data we shall find that the sum of the imipinging forces is
^^ ^ 8.8384 ■.Ii2r ^ (2.5i42r---i)' j The number of oscilla-
^ r 3456/^
tionsisrepresentedbyo^, }^'^\ , + ^.^^ x (^-Si^^^D^
^ ^ (I2.6723r+1) r 12.6723r+l)2
If we take, for an example, the radius to be 1 mile, then the
force acting at the point of contact is=(120.8384 + .0006634)
= 120.839 lbs. per carriage.
As it is evident that the second term of both the above
equations due to the taper of the wheels is scarcely
appreciable except . at very great velocities and round very
sharp curves, it is better to omit it altogether in the estimate;
and then we have the following practical rules adapted to
the data already given :
Rule — To find the, force of impingence on the curve:
Add together 112 and the quotient of 8.838 divided by
the radius in miles : the sum is the resistance due to
the impinging force in pounds common to aU velocities.
Rule — To find the number of oscillations in a second of
time : Divide the nimiber 10.56 by the sum of 1 + 12.67 times
. the radius : the quotient is the number required. If the
number for any other velocity is wanted, multiply this
result by the given velocity, and divide by 30.
G G
282
The oscillations of the wheels computed by the foregoing
rule must not be confounded with the actual oscillations
observed by a passenger travelling in a carriage^ which are
produced by the lateral play of the springs and bearings,
and are much more frequent. It may be easily shown
that the engine is more liable to oscillation than the car-
riages, from its greater weight and the inequality of the
diameters of the wheels and conical tires, also because the
centre of gravity of the machine is higher, and there is an
unequal action produced by the successive reciprocating
motion of the two crank?. But this oscillation is not
communicated to the cstrriages, and since my intention
has been to offer a general rule oi^ily, I shall not take any
account of it.
Since the resistance computed by the foregoing rule is not
uniform but chronic, it is now proper to determine the mean
tractive force required to overcome it. Because the ex-
pression B600 (?^L±ir) represents the force of impingence
of one cforiage, and v x ^•^^^"' represents the oscillations
in a second of time, then 5600 (« + 4) x ?:?33© _. ^^^ ^tole
T
force of impingeujee aeting duriiig this time. But the
lateral velocity with which this force moves is to the ffEwr-
ward velocity as the sine of the length to the radiufi, ^
^ . V :: (?!?L±2tf . am f gr therefore v = V k ??L±ir ;
4mV 2m 2mr
consequently the force with which the whole train r§9ists
uniformly is 5600 (« + 4) V x ii666^mj_2r) . ^^ ^j^^
this expression is simplified to suit the dato* already assumed,
the rule becomes ^-^ x ^^'^7^J' f ^ = uniform maximum
13.676 y*
resistance.
It must be borne in mind that this resistance js tha
greatest which can ever occur, because, by hy^thesis.
283
the extreme lateral play of the wheels was assumed. But
the carriages will oscillate though the lateral motion be
not extreme, and it is required to know what the resistance
will be in any given case. This may be easily accomplished
by observing the number of oscillations made in a second
of time. The resistance wiU vary as the squares of the
sines of the angles of impingenoe. But the angle of
impingence depends upon the ratio of the chord to the
radius of the curve, and this ratio will be obtained by
supposing that the radius varies inversely aa the number
of oscillations, for then it is evident that the length of the
chord being the same, the radius for a less number of
oscillations will be greater, and consequently the angle of
impingence less, and the effect produced will be the same
as if the space travelled over were greater before the wheels
came in contact with the rail; so that we have the following
method to determine the actual resistance :
Let O bQ the observed number of oscillations: when the
radius = 1, the sine = - x ^^ "** ^^ due to O; consequently
the resistance will vary as - ; hence the expression for
the resistance with any observed number of oscillations is
954.54 ^ X (n+4) x C«2+Hr)' ^^ ^gj^g ^^e ^^ta as before,
(n+4) >< ^ X ^iMZH!L±ir = general expression of resistance
in pounds.
Rule — To find the resistance qfa curve {acting unifoimily
to retard motion) : Multiply the number of carriages plus 4
by the square of the oscillations observed in a second, and
by the cube of the sum of 1 + 12.67 times the radius, and
divide this product by 1514 times the square of the radius :
the quotient is the resistance of the train in pounds at a
velocity of 30 miles per hour. For any other velocity divide
this result by the given velocity, and multiply the quotient
by 30, the product is the resistance sought.
284
Example :
Given « = 10 carriages.
0=1 oscillation per second,
r = 1 mile radius,
rrten (10^4 =14) xi»x (12.67^1)3 ^ j^g g^ j^^ resistance.
1514
In treating of this subject^ I am aware that the informa-
tion we possess is by no means satisfactory, and is very
scanty j and indeed, the foregoing estimate of the resistance
I wish the reader to accept as suggestive only. But, were
there a few good experiments made, the calculation might
be reduced to almost a certainty, by the use of the fore-
going investigation. For, if the actual resistance were
ascertained with given dimensions, then a practical rule
can be formed by making the resistance vary directly as
the square of the number of oscillations, the radius, and the
number of carriages ; and inversely as the velocity. When
the resistance is determined for any of the set of wheels,
whose distances are respectively 90, 100, 110, 120, 130
inches, then the resistance due to any other set will vary
inversely as the numbers 2077, 1514, 1137, 876, 689,
respectively, the velocity, radius of curve, number of car-
riages, and number of oscillations per second, remaining
the same in all cases. Also, we derive that the resistance
due to curves is not great, except in extreme cases, and it
need not be generally regarded when the centrifugal force
is properly balanced.
As it may be convenient to know what diflPerence a varia-
tion of the distance between the wheels makes in the
estimate, I subjoin the requisite alterations of the coeffi-
cients employed in the foregoing rules.
285
When the distance is t
[ =c
Instead of the coefficient.
Inches.
Inches.
Inches.
Inches.
90
110
120
130
8.838 substitute.
7.95
9.72
10.60
11.49
12.576 do.
15.08
12.34
11.31
8.29
12.672 do.
15.63
10.47
8.80
7.50
10.560 do.
11.73
9.60
8.80
8.12
1514,000 do.
2077,00
1137.00
876.16
689.18
If it is required to know the resistance caused by oscil-
lation on a straight line, the following form will give it :
Resistance is = ^^ ^^ ^^) ^' in pounds.
The literal expression of the above form may be more
convenient, therefore I herewith subjoin it.
To find the resistance on a straight line due to the oscilla-
tion of the carriages :
Multiply together, the coefficient 106, the number of
carriages plus 4, and the square of the number of oscilla-
tions per second ; divide the product by the velocity in
miles per hour : the quotient is the resistance required in
pounds.
The friction consequent upon the resistance may be
assumed to be ]^th of the result derived from the rules
whether for a curve or for a straight Une.
I shall now conclude this essay; and I beg the reader
to consider that I do not put forth the data I have
adopted as invariable, but have singled them out from
the many practical cases that occur, rather for the sake of
argument. Should the reader be desirous of adopting his
own, or any other practical data, I shall be happy, if in
the preceding pages I have been instrumental as a guide
in leading his inquiries to an approximate, if not an accu-
rate result. Though the consideration of the acceleration
or retardation of trains is a subject which may be properly